Master Gleichstromkreise: 5 Widerstände
Question
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The following quantities appear in the problem:
elektrische Stromstärke \(I\) / elektrische Spannung \(U\) / elektrischer Widerstand \(R\) /
The following formulas must be used to solve the exercise:
\(\sum I = 0 \quad \) \(\sum U = 0 \quad \) \(U=RI \quad \) \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \quad \) \(R = R_1 + R_2 \quad \)
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Exercise:
Bestimme für die folgen Schaltungen den Ersatzwiderstand die von der Spannungsquelle gelieferte Stromstärke die Spannung an jedem Widerstand sowie die Stromstärke durch jeden Widerstand. An allen Schaltungen liegt eine Spannung von UO an. Die Widerstände betragen jeweils R_i i ohm also R_RaO R_RbO etc. center circuitikz %st ROW %%%%%%%%%%%%%%%%%%%%% %B neu a scopexshift-cm yshiftcm draw to battery l^U_ ; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %E neu b scopexshift.cm yshiftcm draw to battery l^U_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %I neu c scopexshiftcm yshiftcm draw to battery l_U_ -; draw - to european resistor l^R_ -; draw - to european resistor l^R_ ; draw - to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% %N neu d scopexshiftcm yshift-cm draw to battery l^U_ ; draw to european resistor l_R_ ; draw to european resistor l_R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %A neu e scopexshiftcm yshift-cm draw . to battery l^U_ .; draw .--; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --.; scope %D neu f scopexshift.cm yshift-cm draw . to battery l_U_ .; draw .--; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --.; scope %rd ROW %%%%%%%%%%%%%%%%%%%%% %F neu g scopexshiftcm yshift-cm draw to battery l^U_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %C neu h scopexshift.cm yshift-cm draw to battery l_U_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %H neu i scopexshiftcm yshift-cm draw - to battery l^U_ ; draw --; draw to european resistor l^R_ -; draw to european resistor l^R_ -; draw ----; draw - to european resistor l^R_ -; draw - to european resistor l^R_ --; draw -- to european resistor l^R_ -; scope circuitikz center
Solution:
abcliste %%%%%%%%%%%%%% Zwei-Zeilen-Fälle %%%%%%%%%%%%%% % --------------------------- %B abc Fall .A: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw to european resistor l^R_ ; draw .---.; draw .---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i & rulmmmmmm BRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm BIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center % --------------------------- %E abc Fall .B: center circuitikz draw - to battery l^U_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw ------; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP & EUeP hline R_i & rulmmmmmm ERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm EIP & EIaP & EIbP & EIcP & EIdP & EIeP hline tabularx center % --------------------------- %I abc Fall .C: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw .---.; draw .---.; draw .---.; draw .---.; draw ---.; draw --.; draw --; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm IUaP & IUbP & IUcP & IUdP & IUeP hline R_i & rulmmmmmm IRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm IIP & IIaP & IIbP & IIcP & IIdP & IIeP hline tabularx center % --------------------------- %NEU! abc Fall .D: center circuitikz scope draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw - to european resistor l_R_ -; draw - to european resistor l_R_ -; scope circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i & rulmmmmmm BRP& cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmmBIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center %%%%%%%%%%%%%% "Drei"-Zeilen-Fälle %%%%%%%%%%%%%% %A abc Fall .A: center circuitikz draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw - to european resistor l^R_ -; draw -.--.; draw -.--.; draw -----; draw ---; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm AUaP & AUbP & AUcP & AUdP & AUeP hline R_i & rulmmmmmm ARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm AIP & AIaP & AIbP & AIcP & AIdP & AIeP hline tabularx center % --------------------------- %D abc Fall .B: center circuitikz draw - to battery l^U_ ; draw --; draw --; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw ------; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm DUaP & DUbP & DUcP & DUdP & DUeP hline R_i & rulmmmmmm DRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm DIP & DIaP & DIbP & DIcP & DIdP & DIeP hline tabularx center % --------------------------- %F abc Fall .C: center circuitikz draw . to european resistor l^R_ .; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw .--; draw to european resistor l^R_ ; draw --.--..--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP & FUeP hline R_i & rulmmmmmm FRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm FIP & FIaP & FIbP & FIcP & FIdP & FIeP hline tabularx center %%%%%%%%%%%%%% "Vier"-Zeilen-Fälle %%%%%%%%%%%%%% %C abc Fall .A: center circuitikz draw to european resistor l^R_ ; draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw to european resistor l^R_ ; draw -. to european resistor l^R_ -.; draw -.----; draw .--.; draw .--.; draw ---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP & CUeP hline R_i & rulmmmmmm CRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm CIP & CIaP & CIbP & CIcP & CIdP & CIeP hline tabularx center abc Fall H: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw .---.; draw .---.; draw .---.; draw .---.; draw ---.; draw --.; draw --; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm IUaP & IUbP & IUcP & IUdP & IUeP hline R_i & rulmmmmmm IRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm IIP & IIaP & IIbP & IIcP & IIdP & IIeP hline tabularx center abcliste
Bestimme für die folgen Schaltungen den Ersatzwiderstand die von der Spannungsquelle gelieferte Stromstärke die Spannung an jedem Widerstand sowie die Stromstärke durch jeden Widerstand. An allen Schaltungen liegt eine Spannung von UO an. Die Widerstände betragen jeweils R_i i ohm also R_RaO R_RbO etc. center circuitikz %st ROW %%%%%%%%%%%%%%%%%%%%% %B neu a scopexshift-cm yshiftcm draw to battery l^U_ ; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %E neu b scopexshift.cm yshiftcm draw to battery l^U_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %I neu c scopexshiftcm yshiftcm draw to battery l_U_ -; draw - to european resistor l^R_ -; draw - to european resistor l^R_ ; draw - to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% %N neu d scopexshiftcm yshift-cm draw to battery l^U_ ; draw to european resistor l_R_ ; draw to european resistor l_R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; scope %A neu e scopexshiftcm yshift-cm draw . to battery l^U_ .; draw .--; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --.; scope %D neu f scopexshift.cm yshift-cm draw . to battery l_U_ .; draw .--; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --.; scope %rd ROW %%%%%%%%%%%%%%%%%%%%% %F neu g scopexshiftcm yshift-cm draw to battery l^U_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %C neu h scopexshift.cm yshift-cm draw to battery l_U_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %H neu i scopexshiftcm yshift-cm draw - to battery l^U_ ; draw --; draw to european resistor l^R_ -; draw to european resistor l^R_ -; draw ----; draw - to european resistor l^R_ -; draw - to european resistor l^R_ --; draw -- to european resistor l^R_ -; scope circuitikz center
Solution:
abcliste %%%%%%%%%%%%%% Zwei-Zeilen-Fälle %%%%%%%%%%%%%% % --------------------------- %B abc Fall .A: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw to european resistor l^R_ ; draw .---.; draw .---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i & rulmmmmmm BRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm BIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center % --------------------------- %E abc Fall .B: center circuitikz draw - to battery l^U_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw ------; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP & EUeP hline R_i & rulmmmmmm ERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm EIP & EIaP & EIbP & EIcP & EIdP & EIeP hline tabularx center % --------------------------- %I abc Fall .C: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw .---.; draw .---.; draw .---.; draw .---.; draw ---.; draw --.; draw --; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm IUaP & IUbP & IUcP & IUdP & IUeP hline R_i & rulmmmmmm IRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm IIP & IIaP & IIbP & IIcP & IIdP & IIeP hline tabularx center % --------------------------- %NEU! abc Fall .D: center circuitikz scope draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw - to european resistor l_R_ -; draw - to european resistor l_R_ -; scope circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i & rulmmmmmm BRP& cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmmBIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center %%%%%%%%%%%%%% "Drei"-Zeilen-Fälle %%%%%%%%%%%%%% %A abc Fall .A: center circuitikz draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw - to european resistor l^R_ -; draw -.--.; draw -.--.; draw -----; draw ---; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm AUaP & AUbP & AUcP & AUdP & AUeP hline R_i & rulmmmmmm ARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm AIP & AIaP & AIbP & AIcP & AIdP & AIeP hline tabularx center % --------------------------- %D abc Fall .B: center circuitikz draw - to battery l^U_ ; draw --; draw --; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw ------; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm DUaP & DUbP & DUcP & DUdP & DUeP hline R_i & rulmmmmmm DRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm DIP & DIaP & DIbP & DIcP & DIdP & DIeP hline tabularx center % --------------------------- %F abc Fall .C: center circuitikz draw . to european resistor l^R_ .; draw --; draw --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw to european resistor l^R_ ; draw .--; draw to european resistor l^R_ ; draw --.--..--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP & FUeP hline R_i & rulmmmmmm FRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm FIP & FIaP & FIbP & FIcP & FIdP & FIeP hline tabularx center %%%%%%%%%%%%%% "Vier"-Zeilen-Fälle %%%%%%%%%%%%%% %C abc Fall .A: center circuitikz draw to european resistor l^R_ ; draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw to european resistor l^R_ ; draw -. to european resistor l^R_ -.; draw -.----; draw .--.; draw .--.; draw ---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP & CUeP hline R_i & rulmmmmmm CRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm CIP & CIaP & CIbP & CIcP & CIdP & CIeP hline tabularx center abc Fall H: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw .---.; draw .---.; draw .---.; draw .---.; draw ---.; draw --.; draw --; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i & cellcolorgray.UO & rulmmmmmm IUaP & IUbP & IUcP & IUdP & IUeP hline R_i & rulmmmmmm IRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i & rulmmmmmm IIP & IIaP & IIbP & IIcP & IIdP & IIeP hline tabularx center abcliste