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 = 53 Ω, R₃ = 72 Ω and R₄ = 117 Ω. The capacitance is C = 35 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

What is I_C,max(open), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is open? A positive value for the current is defined to be in the direction of the arrow shown.

Answer 1

Charge on the capacitor after switch has been closed for very longtime ,at t=infinity capacitor will act as open circuit,so voltage across capacitor is voltage across R3.

V₃=12*72/(53+72+117)=3.57 Volts

Charge

Q(infinity)=3.57*35=124.96 uC

Therefore

I_C,max(open)=-Q(infinty)/T =-Q_infinity/(R₂+R₃)C =-124.96/(53+72)*35

I_C,max(open)=-0.02856 A