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University Physics Volume 2

# Key Equations

### Key Equations

 Terminal voltage of a single voltage source $Vterminal=ε−IreqVterminal=ε−Ireq$ Equivalent resistance of a series circuit $Req=R1+R2+R3+⋯+RN−1+RN=∑i=1NRiReq=R1+R2+R3+⋯+RN−1+RN=∑i=1NRi$ Equivalent resistance of a parallel circuit $Req=(1R1+1R2+⋯+1RN)−1=(∑i=1N1Ri)−1Req=(1R1+1R2+⋯+1RN)−1=(∑i=1N1Ri)−1$ Junction rule $∑ Iin=∑ Iout∑ Iin=∑ Iout$ Loop rule $∑ V=0∑ V=0$ Terminal voltage of N voltage sources in series $Vterminal=∑i=1Nεi−I∑i=1Nri=∑i=1Nεi−IreqVterminal=∑i=1Nεi−I∑i=1Nri=∑i=1Nεi−Ireq$ Terminal voltage of N voltage sources in parallel $Vterminal=ε−I∑i=1N(1ri)−1=ε−IreqVterminal=ε−I∑i=1N(1ri)−1=ε−Ireq$ Charge on a charging capacitor $q(t)=Cε(1−e−tRC)=Q(1−e−tτ)q(t)=Cε(1−e−tRC)=Q(1−e−tτ)$ Time constant $τ=RCτ=RC$ Current during charging of a capacitor $I=εRe−tRC=Ioe−tRCI=εRe−tRC=Ioe−tRC$ Charge on a discharging capacitor $q(t)=Qe−tτq(t)=Qe−tτ$ Current during discharging of a capacitor $I(t)=−QRCe−tτI(t)=−QRCe−tτ$
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