A circuit is constructed with four resistors, one capacitor, one battery and a s

Question

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 79 ?, R3 = 108 ? and R4 = 123 ?. The capacitance is C = 42 ?F and the battery voltage is V = 24 V.

1. The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

2. What is I1(?), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?

3. What is Q(?), the charge on the capacitor after the switch has been closed for a very long time?

Explanation / Answer

1.) at t=0 capacitor will act as a short circuit

so I1(0) = V/(R1+R4) = 24/(79+123) = 0.118 A

2.) at t= infinite capacitor will act as a open circuit

so I1(infinite) = V/(R1+R2+R3+R4) = 24/(79+79+108+123) = 0.061 A

3.) voltage across capacitor Vc = V - [(R1+R4)*I1(infinite)] = 24 - [202*0.061] = 11.678 v

so charge Q(infinite) = C*Vc = 42*10^-6*11.678 = 490.476 micro Coulomb

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