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 = 51 ?, R3 = 80 ? and R4 = 109 ?. The capacitance is C = 49 ?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?

4)Consider the circuit above, with R5 = 99 ? 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?

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 51 ?, R3 = 80 ? and R4 = 109 ?. The capacitance is C = 49 ?F and the battery voltage is V = 24 V. 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? Consider the circuit above, with R5 = 99 ? 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? 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

1) t = 0 Capacitor is behaving like a short circuit. That means R1 and R4 is in series.
Rea = R1+R4 = 160ohm
Current = Voltage/Req = 24/160 = 3/20 = 0.15 Amp Same current will pass through R1 too.

2) After a very long time capcitor will be open circuit hence
Req = R1+R2+R3+R4 = 291 ohm
Current = Voltage/Req = 24/291 = 0.0824 Amp Same current will pass through R1 too.

3) Potential across Capacitor after a long time = Potential across Combined R2+R3 = i(t = inf) *(R2+R3) = 10.80Volt

Q - C * V = 49 * 10.8 u = 529.4 uC

4) Req will change intially. As Capacitor is short circuit
So R5 is parallal to (R2+R3) = 56.38 Ohm

This will be in series with R1 and R4 Hence Total Req = 216.38 Ohm

Current = Voltage/Req = 24/216.38 = 0.111 Amp Same current will pass through R1 too.

5)
After long time Capcitor will be open circuit hence no current willl pass through R5.
So Potential across capacitor will be same. Hence Charge will be same. = 529.4uC

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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