Consider the circuit pictured. The switch has been opened for a long time T-> in
ID: 1287504 • Letter: C
Question
Consider the circuit pictured. The switch has been opened for a long time T-> infinity and then is suddenly closed.
(a) (4 points) Find the current through the 50 ohm resistor immediately after the switch is closed.
(b) (6 points) Find the potential difference Vcd a long time after closing the switch.
Consider now a capacitor charged initially to 12nanoC (1*10^-6C) and then connected to a resistance of 3.4 Mohm.
(c) (4 points) The switch is closed and 4s later the charge in the capacitor has dropped to 3nanoC. Determine the capacitance C of the capacitor.
(d) (6 points) Determine the total amount of energy dissipated in the resistor during that time.
Please show all equations and steps to get best answer.
Consider the circuit pictured. The switch has been opened for a long time and then is suddenly closed. Find the current through the 50 Ohm resistor immediately after the switch is closed. Consider now a capacitor charged initially to 12 mu C and then connected to a resistance of 3.4 M Ohm. The switch is closed and 4 s later the charge in the capacitor has dropped to 3muC. Determine the capacitance C of the capacitor.Explanation / Answer
a)
Immediatley after switch is closed Capacitot acts as short circuit ,so Current through 50 ohms is
equivalent resistance
Req=100+(75*50/75+50)=130 ohms
Total Current flowing in the circuit is
I=V/Req=150/130 =1.154 A
Current through 50 ohms by current divider rule is
I50=I*(75/75+50) =1.154*(75/125)
I50=0.692 A
b)
After long time switch is closed capacitor acts as open circuit ,so voltage across 100 ohms is
V100=V*(100/100+50) =150*(2/3)
V100=100 Volts
so potential difference across capacitor is
Vcd=V100=100 Volts
c)
Charge as a function of time in RC circuit is
Q=Qoe-t/T
3=12*e-4/T
ln(0.25)=-4/T
T=2.885 sec
since time constant
T=R*C
2.885=3.4*106*C
C=8.486*10-7 F or 0.8486 uF or 848.6 nF
d)
Emergy dissipated in resistor is
E=(1/2)(Qo2-Q)/C =(1/2)(122-32)*10-12/(8.486*10-7)
E=7.95*10-5 J