In the above complex circuit, the constant perfect battery has been connected fo

Question

In the above complex circuit, the constant perfect battery has been connected for a large period of time so that the currents all have steady values. Given these facts, calculate each of the following: The current flowing through the 9-ohm resistor. (2) The current flowing in the 8-ohm resistor. (2) The potential difference (Voltage) across the 30-microfarad capacitor. (2) The potential energy stored in the 30-microfarad capacitor. (1) At some later time, the connection at point P breaks, causing the current in the 9-ohm resistor to becomes zero. Calculate the total amount of heat energy dissipated in the 8-ohm resistor after the connection fails. (3)

Explanation / Answer

Here , after a very long time

as the capacitor will behave as an open circuit

a) for the net resistance

R = 8 + 4 * (4 + 8)/(4 + 8 + 4)

R = 11 Ohm

current through 9 ohm = 120/R

current through 9 ohm = 120/11 A

b)

Current in 8 Ohm = 120/11 * 4/(4 + 8+ 4)

Current in 8 Ohm = 2.72 A

c)

V(30 uF) = 4 * (2.72) V

V(30 uF) = 10.88 V

d)

energy in 30 uF capacitor = 0.5 * C * V^2

energy in 30 uF capacitor = 0.5 * 10.88^2 * 30 *10^-6

energy in 30 uF capacitor = 1.775 *10^-3 J

the energy in 30 uF capacitor is 1.775 *10^-3 J

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