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in Physics by (56.9k points)

In the circuit shown, the switch S is open and the capacitor (C = 2.5 μF) is initially uncharged. The switch is then closed long enough to allow the capacitor to fully charge. If the switch is now opened, how much time (in μsec) is required for the potential difference across the capacitor to reach 2 V? 

(1) 27 

(2) 1.9 

(3) 5.2 

(4) 40 

(5) 22 

1 Answer

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Best answer

Correct option: (1) 27

Explanation:

When the capacitor is fully charged, the voltage across it is 15 V. After the switch is opened, it discharges through a resistor combination equivalent to 5.33 Ω. The equation describing the voltage on the capacitor is 15 exp / 2 (− t / RC ), which yields t = (5.33) (2.5) In (15 / 2)  27μs.

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