The switch has been open for a long time when at time t 0 t

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?

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

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

Continuing with the new circuit, what is Q(?), the charge on the capacitor after the switch has been closed for a very long time?

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1-R2-46 , R3 ·75 and R4-106 . The capacitance is C·41 F and the battery voltage is V-24 V Ra R4

Solution

3.

a)

Just after switch is closed capacitor acts as short circuit ,so Current flowing through R1 is

I₁(0) =V/R_eq =V/(R₁+R₄)

I₁(0) =24/(46+106)

I₁(0) =0.158 A

b)

After Long time capacitor acts as open circuit ,so current flowing through R1 is

I₁ =V/(R₁+R₂+R₃+R₄)

I₁=24/(46+46+75+106)

I₁=0.088 A

c)

Voltage across Capacitor

V_C=V₂₃ =I*(R₂+R₃) =0.088 (46+75)

V_C=10.64 Volts

Charge

Q=CV_C =41*10^-6*10.64

Q=4.36*10^-4C

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4.

a)

Just after switch is closed capacitor acts as short circuit ,so Current flowing through R1 is

I₁(0) =V/R_eq =V/(R₁+R₄+R₅)

I₁(0) =24/(46+106+96)

I₁(0) =0.0968 A