Proficient Gleichstromkreise: 4 Widerstände
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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 %%%%%%%%%%%%%%%%%%%%% %Ab 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 --; scope %Ba 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 --; draw to european resistor l^R_ ; draw --; scope %Ce 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 ----; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% %Dneu 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_ --; scope %Ef scopexshift.cm 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 --; scope %Fc 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_ ; scope circuitikz center
Solution:
abcliste % ------------------------------------------- %Bneua 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 -.--.; draw -.--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP hline R_i/siohm & rulmmmmmmBRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmBIP & BIaP & BIbP & BIcP & BIdP hline tabularx center % ------------------------------------------- %Aneub abc Fall .B: 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 -.--.; draw -.--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmmAUaP & AUbP & AUcP & AUdP hline R_i/siohm & rulmmmmmmARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmAIP & AIaP & AIbP & AIcP & AIdP hline tabularx center % ------------------------------------------- %Eneuc 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 ---; draw ---; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP hline R_i/siohm & rulmmmmmmERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmEIP & EIaP & EIbP & EIcP & EIdP hline tabularx center % ------------------------------------------- % neud abc Fall .D mit Verhältnissen! 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 .---.; draw .---.; circuitikz center % ------------------------------------------- %Fneue 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 --; draw --; draw --.; draw --.; draw .--.; draw .--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP hline R_i/siohm & rulmmmmmmFRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmFIP & FIaP & FIbP & FIcP & FIdP hline tabularx center % ------------------------------------------- %Cneuf abc Fall .A: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw -.--.; draw -.--.; draw to european resistor l^R_ ; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP hline R_i/siohm & rulmmmmmmCRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmCIP & CIaP & CIbP & CIcP & CIdP 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 %%%%%%%%%%%%%%%%%%%%% %Ab 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 --; scope %Ba 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 --; draw to european resistor l^R_ ; draw --; scope %Ce 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 ----; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% %Dneu 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_ --; scope %Ef scopexshift.cm 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 --; scope %Fc 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_ ; scope circuitikz center
Solution:
abcliste % ------------------------------------------- %Bneua 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 -.--.; draw -.--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP hline R_i/siohm & rulmmmmmmBRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmBIP & BIaP & BIbP & BIcP & BIdP hline tabularx center % ------------------------------------------- %Aneub abc Fall .B: 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 -.--.; draw -.--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmmAUaP & AUbP & AUcP & AUdP hline R_i/siohm & rulmmmmmmARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmAIP & AIaP & AIbP & AIcP & AIdP hline tabularx center % ------------------------------------------- %Eneuc 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 ---; draw ---; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP hline R_i/siohm & rulmmmmmmERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmEIP & EIaP & EIbP & EIcP & EIdP hline tabularx center % ------------------------------------------- % neud abc Fall .D mit Verhältnissen! 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 .---.; draw .---.; circuitikz center % ------------------------------------------- %Fneue 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 --; draw --; draw --.; draw --.; draw .--.; draw .--.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP hline R_i/siohm & rulmmmmmmFRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmFIP & FIaP & FIbP & FIcP & FIdP hline tabularx center % ------------------------------------------- %Cneuf abc Fall .A: center circuitikz draw . to european resistor l^R_ .; draw . to european resistor l^R_ .; draw -. to european resistor l^R_ -.; draw -.--.; draw -.--.; draw to european resistor l^R_ ; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|hline & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP hline R_i/siohm & rulmmmmmmCRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmCIP & CIaP & CIbP & CIcP & CIdP hline tabularx center % ------------------------------------------- abcliste