Proficient Gleichstromkreise: 4 Widerstände
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
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:
\(\sum I = 0 \quad \) \(\sum U = 0 \quad \) \(U=RI \quad \) \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \quad \) \(R = R_1 + R_2 \quad \)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
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 %%%%%%%%%%%%%%%%%%%%% 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 --; draw to european resistor l^R_ ; draw --; scope scopescalexshift.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 --; scope scopexshiftcm 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_ ; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% 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 ----; 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 ----; 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 --; 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 -.--.; 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 %B 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 & 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 % C abc Fall C: 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 %D 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 & rulmmmmmm DUaP & DUbP & DUcP & DUdP hline R_i/siohm & rulmmmmmmDRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmDIP & DIaP & DIbP & DIcP & DIdP hline tabularx center 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 ---; 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 abc Fall F: 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 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 %%%%%%%%%%%%%%%%%%%%% 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 --; draw to european resistor l^R_ ; draw --; scope scopescalexshift.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 --; scope scopexshiftcm 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_ ; scope %nd ROW %%%%%%%%%%%%%%%%%%%%% 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 ----; 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 ----; 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 --; 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 -.--.; 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 %B 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 & 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 % C abc Fall C: 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 %D 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 & rulmmmmmm DUaP & DUbP & DUcP & DUdP hline R_i/siohm & rulmmmmmmDRP & cellcolorgray.RaO& cellcolorgray.RbO & cellcolorgray.RcO & cellcolorgray.RdO hline I_i/siA & rulmmmmmmDIP & DIaP & DIbP & DIcP & DIdP hline tabularx center 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 ---; 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 abc Fall F: 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 abcliste