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 = 72 ?, R3 = 61 ? and R4 = 99 ?. The capacitance is C = 68 ?F and the battery voltage is V = 24 V.

4?Consider the circuit above, with R5 = 89 ? in series with the capacitor. Once again, 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?

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

Explanation / Answer

Just after switch is closed capacitor acts as short circuit ,so equivalent resistance

Req =R1+R4+(R5 ||(R2+R3))

Req =72+99 +(89*133/89+133)

Req=224.32 ohms

so current in the circuit

I1(0)=V/Req =24/224.32

I1(0)=0.107 A

5)

After long time capacitor acts as open circuit ,so current through the circuit

I1=V/(R1+R2+R3+R4)

I1=24/(72+99+61+72)

I1=0.07895 A

so Voltage across capacitor is

Vc=I*(R2+R3) =0.07895*(72+61)

Vc=10.5 Volts

so charge on capacitor is

Q=C*Vc =10.5*68u

Q=714 uC

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.