You connect a battery, resistor, and capacitor as in (Figure 1) , where E = 56.0

ID: 1408155 • Letter: Y

Question

You connect a battery, resistor, and capacitor as in (Figure 1) , where E = 56.0 V , C = 5.00 ?F , and R = 140 ? . The switch S is closed at

t = 0.

A) When the voltage across the capacitor is 8.00 V, what is the magnitude of the current in the circuit?

Express your answer with the appropriate units.

B) At what time t after the switch is closed is the voltage across the capacitor 8.00 V?

Express your answer with the appropriate units.

C) When the voltage across the capacitor is 8.00 V, at what rate is energy being stored in the capacitor?

Express your answer with the appropriate units.

Will rate. Thank you!

A) When capacitor voltage is 8V, resistor potential difference is 56-8 =48V

current i = 48V/140 Ohm = 0.343 A

B) V = Vo (1- e^-t/RC)

8 = 56 (1 - e^-t/RC)

8/56 = 1 - e^-t/(140*5*10^-6)

-t/(140*5*10^-6) = ln(1-8/56)

t = - (140*5*10^-6) ln(1-8/56)

= 0.000108 s

C) rate at which energy is being stored = d(0.5 CV^2) /dt

= C*V dV/dt

= C*8 * Vo (e^-t/RC) /RC

= 8*(56-8) /140

= 8*48/140 = 2.743 J

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