Question

The switch in the circuit shown has been closed for a long time and is opened at t = 0. Find a) the initial value of v(t), b) the time constant for t > 0, the numerical expression for i(t) after the switch has been opened, the initial energy stored in the capacitor, and the length of time required to dissipate 75% of the initially stored energy. 20 kΩ 75 mA 80 kΩ 0.4 µF 50 kΩ Answer: (a) 200 V; (b) 20 ms; (c) 200e^-50t V, t >= 0; (d) 8 mJ; (e) 13.86 ms

Name: 73 the switch in the circuit shown has been closed for a long time and is opened at t 0 find a the initial value of vt b the time constant for t 0 the numerical expression for t after the sw 05874
Uploaded: 2022-01-11T18:04:06-08:00
Duration: 7 min 56 s
Channel: Manish Jain
Description: 73 the switch in the circuit shown has been closed for a long time and is opened at t 0 find a the initial value of vt b the time constant for t 0 the numerical expression for t after the sw 05874

          The switch in the circuit shown has been closed for a long time and is opened at t = 0. Find a) the initial value of v(t), b) the time constant for t > 0, the numerical expression for i(t) after the switch has been opened, the initial energy stored in the capacitor, and the length of time required to dissipate 75% of the initially stored energy.

20 kΩ
75 mA
80 kΩ
0.4 µF
50 kΩ

Answer: (a) 200 V; (b) 20 ms; (c) 200e^-50t V, t >= 0; (d) 8 mJ; (e) 13.86 ms

Added by Megan C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Manish Jain

01/11/2022

Step 1

Since the switch has been closed for a long time, the circuit has reached a steady state and the capacitor is fully charged. The voltage across the capacitor is equal to the current through the 20 kΩ resistor times the resistance, which is (75 mA)(20 kΩ) = 1500 V. Show more…

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The switch in the circuit shown has been closed for a long time and is opened at t = 0. Find a) the initial value of v(t), b) the time constant for t > 0, the numerical expression for i(t) after the switch has been opened, the initial energy stored in the capacitor, and the length of time required to dissipate 75% of the initially stored energy. 20 kΩ 75 mA 80 kΩ 0.4 µF 50 kΩ Answer: (a) 200 V; (b) 20 ms; (c) 200e^-50t V, t >= 0; (d) 8 mJ; (e) 13.86 ms