In the circuit shown below epsilon1 240 V epsilon2 120 V1

In the circuit shown below, epsilon_1 = 24.0 V, epsilon_2 = 12.0 V_1 R_1 = 70.0 Ohm and R_3 = 20.0 Ohm What is the current i_3F? An RC circuit is hooked up to a battery as shown in the figure below, with R = 636.0 Ohm. C = 25.0 mu F and the battery has and epsilon = 45.0 V. What is the time constant for this circuit? For the circuit in the previous problem, if the capacitor is initially uncharged and the switch is closed at time t = 0. what is the charge on the capacitor at time t = 1.54times 10^-2 s? For the circuit in the previous problem, what is the current through the circuit at t 1.54times 10^-2 s after the switch is closed? For the circuit in the previous problem, what is the voltage across the capacitor at t - 1.54times 10^-2 s after the switch is closed?

Solution

9.

Applying Kirchoff\'s Loop rule on right loop

E₂-I₃R₃=0

I₃=E₂/R₃ =12/20

I₃=0.6 A

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10.

TIme Constant

T=RC =636*(25*10^-6)

T=0.0159 s or 15.9 ms

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11.

Maximum charge

Q_max=CE =25*45 =1125 uC

In a RC circuit charge as a function as a time for charging is given by

Q=Q_max[1-e^-t/T] =1125[1-e^{-0.0154/0.0159}]

Q=698 uC or 6.98*10^-4 C

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12.

Maximum current

I_max=E/R =45/636 =0.07075 A

In a RC circuit current as a function as a time for charging is given by

I=I_max[e^-t/T] =0.07075[e^{-0.0154/0.0159}]

I=0.02686 A

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13.

In a RC circuit voltage as a function of time is given by

V=E[1-e^-t/T] =45[1-e^{-0.0154/0.0159}]

V=27.92 Volts

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