The circuit below was at position a for a long time. It is suddenly switched to
ID: 1491265 • Letter: T
Question
The circuit below was at position a for a long time. It is suddenly switched to position b at time t=0.
(A) Determine whether each of the following statements are true or false.
- The current through the resistor equals the current through the capacitor at all times.
- In the instant after the switch is thrown the voltage across the resistor is zero.
- In the instant after the switch is thrown, the voltage across the capacitor is zero.
- In the instant after the switch is thrown the current through the capapacitor is zero.
(B) If the battery provides a voltage V = 3.50 V, the capacitor has C = DIS(C:1f) C and the resistor has R = 300.0 , what is the capacitor voltage Vc at time t = 1.0 ms?
(C) What is the total energy dissipated in the resistor after time t = 0?
(D) Consider the case when the switch is in position b for a long time, then switched to position a at time t = 0. What is the capacitor voltage Vc at time t = 0.8 ms?
Explanation / Answer
A) The current through the resistor equals the current through the capacitor at all times. - True
In the instant after the switch is thrown the voltage across the resistor is zero. - False
In the instant after the switch is thrown, the voltage across the capacitor is zero. - False
In the instant after the switch is thrown the current through the capapacitor is zero. - False
B) the capacitor voltage Vc at time t = 1.0 ms = 3.50 * (e-1/(0.3))
= 0.1248 V
C) total energy dissipated in the resistor after time t = 0 = 1/2 * 1 * 10-6 * 3.50 * 3.50
= 6.125 * 10-6 J
D) capacitor voltage Vc at time t = 0.8 ms = 3.50 * (1 - e-0.8/(0.3))
= 3.256 V
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