Problem 13: Charging a Capacitor: An RC circuit includes a basic switch. In position "a", the battery, resistor and capacitor are connected in series, and the capacitor charges. In position "b", the battery is replaced with a short, and the capacitor will discharge. Two voltmeters and an ammeter have been added to the circuit. A) Assume that the capacitor is initially uncharged, and then the switch is closed to position "a" at time t0. Which of these equations is a correctly written integral expression including the correct limits? (Recall the shorthand notation for the time constant introduced in the previous step, τ=RC) B) Enter an expression for the charge as a function of time. C) What is the maximum value of the current after the switch is closed?
Problem 13: Charging a Capacitor: An RC circuit includes a basic switch. In position "a", the battery, resistor and capacitor are connected in series, and the capacitor charges. In position "b", the battery is replaced with a short, and the capacitor will discharge. Two voltmeters and an ammeter have been added to the circuit.
A) Assume that the capacitor is initially uncharged, and then the switch is closed to position "a" at time t0. Which of these equations is a correctly written integral expression including the correct limits? (Recall the shorthand notation for the time constant introduced in the previous step, τ=RC)
B) Enter an expression for the charge as a function of time.
C) What is the maximum value of the current after the switch is closed?
D) Enter an expression for the current as a function of time. Your answer must explicitly reference the maximum current, Imax, that was determined in the previous step.
E) Enter an expression for the voltage measured across the resistor, VR, as a function of time.
F) Enter an expression for the voltage measured across the capacitor, VC, as a function of time.
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