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 %%%%%%%%%%%%%%%%%%%%% %cgh / abc scopexshift-.cm yshiftcm 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 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 scopexshift.cm yshiftcm 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 %nd ROW %%%%%%%%%%%%%%%%%%%%% %ijk / def 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 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 to european resistor l^R_ ; scope 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 --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %rd ROW %%%%%%%%%%%%%%%%%%%%% %m scopexshiftcm yshift-cm draw - to european resistor l^R_ ; draw --; 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_ -; scope 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 %https://www.texercises.com/exercise/edit/gleichstrom-doppel-sudoku-v 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 %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/siV & cellcolorgray.UO & rulmmmmmm AUaP & AUbP & AUcP & AUdP & AUeP hline R_i/siohm & rulmmmmmm ARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm AIP & AIaP & AIbP & AIcP & AIdP & AIeP hline tabularx center %B 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 .---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i/siohm & rulmmmmmm BRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm BIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center %C abc Fall E: 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/siV & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP & CUeP hline R_i/siohm & rulmmmmmm CRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm CIP & CIaP & CIbP & CIcP & CIdP & CIeP hline tabularx center %D abc Fall F: 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/siV & cellcolorgray.UO & rulmmmmmm DUaP & DUbP & DUcP & DUdP & DUeP hline R_i/siohm & rulmmmmmm DRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm DIP & DIaP & DIbP & DIcP & DIdP & DIeP hline tabularx center %E abc Fall G: 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/siV & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP & EUeP hline R_i/siohm & rulmmmmmm ERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm EIP & EIaP & EIbP & EIcP & EIdP & EIeP hline tabularx center %F abc Fall B: 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/siV & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP & FUeP hline R_i/siohm & rulmmmmmm FRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm FIP & FIaP & FIbP & FIcP & FIdP & FIeP hline tabularx center %G abc Fall B: 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/siV & cellcolorgray.UO & rulmmmmmm GUaP & GUbP & GUcP & GUdP & GUeP hline R_i/siohm & rulmmmmmm GRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm GIP & GIaP & GIbP & GIcP & GIdP & GIeP hline tabularx center %H 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/siV & cellcolorgray.UO & rulmmmmmm HUaP & HUbP & HUcP & HUdP & HUeP hline R_i/siohm & rulmmmmmm HRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm HIP & HIaP & HIbP & HIcP & HIdP & HIeP hline tabularx center %I 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 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 %%%%%%%%%%%%%%%%%%%%% %cgh / abc scopexshift-.cm yshiftcm 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 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 scopexshift.cm yshiftcm 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 %nd ROW %%%%%%%%%%%%%%%%%%%%% %ijk / def 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 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 to european resistor l^R_ ; scope 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 --; draw to european resistor l^R_ ; draw to european resistor l^R_ ; scope %rd ROW %%%%%%%%%%%%%%%%%%%%% %m scopexshiftcm yshift-cm draw - to european resistor l^R_ ; draw --; 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_ -; scope 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 %https://www.texercises.com/exercise/edit/gleichstrom-doppel-sudoku-v 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 %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/siV & cellcolorgray.UO & rulmmmmmm AUaP & AUbP & AUcP & AUdP & AUeP hline R_i/siohm & rulmmmmmm ARP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm AIP & AIaP & AIbP & AIcP & AIdP & AIeP hline tabularx center %B 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 .---.; circuitikz center center tabularxtextwidth|X||r|r|r|r|r|r|hline & i & i & i & i & i & i hlinehline U_i/siV & cellcolorgray.UO & rulmmmmmm BUaP & BUbP & BUcP & BUdP & BUeP hline R_i/siohm & rulmmmmmm BRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm BIP & BIaP & BIbP & BIcP & BIdP & BIeP hline tabularx center %C abc Fall E: 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/siV & cellcolorgray.UO & rulmmmmmm CUaP & CUbP & CUcP & CUdP & CUeP hline R_i/siohm & rulmmmmmm CRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm CIP & CIaP & CIbP & CIcP & CIdP & CIeP hline tabularx center %D abc Fall F: 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/siV & cellcolorgray.UO & rulmmmmmm DUaP & DUbP & DUcP & DUdP & DUeP hline R_i/siohm & rulmmmmmm DRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm DIP & DIaP & DIbP & DIcP & DIdP & DIeP hline tabularx center %E abc Fall G: 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/siV & cellcolorgray.UO & rulmmmmmm EUaP & EUbP & EUcP & EUdP & EUeP hline R_i/siohm & rulmmmmmm ERP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm EIP & EIaP & EIbP & EIcP & EIdP & EIeP hline tabularx center %F abc Fall B: 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/siV & cellcolorgray.UO & rulmmmmmm FUaP & FUbP & FUcP & FUdP & FUeP hline R_i/siohm & rulmmmmmm FRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm FIP & FIaP & FIbP & FIcP & FIdP & FIeP hline tabularx center %G abc Fall B: 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/siV & cellcolorgray.UO & rulmmmmmm GUaP & GUbP & GUcP & GUdP & GUeP hline R_i/siohm & rulmmmmmm GRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm GIP & GIaP & GIbP & GIcP & GIdP & GIeP hline tabularx center %H 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/siV & cellcolorgray.UO & rulmmmmmm HUaP & HUbP & HUcP & HUdP & HUeP hline R_i/siohm & rulmmmmmm HRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO & cellcolorgray.ReO hline I_i/siA & rulmmmmmm HIP & HIaP & HIbP & HIcP & HIdP & HIeP hline tabularx center %I 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 abcliste