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

Question

A circuit is constructed with three resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R_1 = 30 Ohm, R_2 = R_3 = 60 Ohm. The capacitance is C = 63 muF and the battery voltage is 12 V. (a) The switch has been open for a long time. Then, at time t = 0, the switch is closed. What is I_3(0), the magnitude of the current through the resistor R_3 just after the switch is closed? (b) What is I_3(infinity), the magnitude of the current through the resistor R_3 after the switch has been closed for a very long time? (c) What is Q(infinity), the charge on the capacitor after the switch has been closed for a very long time?

Explanation / Answer

a) just after the switch is closed the capacitor will act as shorted

thus

current I through battery is I = E/(R1 +(R2*R3/R2+R3)) = 12/(30+30) = 1/5 ampere

hence

I3(0) = (1/5)*60/120 = 0.1 ampere

b) after the switch has been closed for long time the capaciotr will acts as open

hence

I3(infinty) = 12/(30+60) = 12/90 = 0.133 ampere

c) charge on capacitor Q = C*V

here c= 63uF

V = 0.133*60 = 8 volt

Q = 63*8 = 0.504*10-3 Columb

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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