Assume that the capacitor in Figure 15-75 is degraded to a point where its leakage resistance is 10 kΩ. Determine the output voltage under the degraded condition.

Question

Accepted Answer

The effective circuit resistance is

[latex]R_{th}= \frac{RR_{leak}}{R+ R_{leak}} = \frac{(4.7 \ k\Omega )(10 \ k\Omega )}{14.7 \ k\Omega }= 3.20 \ k\Omega [/latex]

To determine the output voltage, find the Thevenin equivalent voltage.

[latex]V_{th}= \left(\frac{R_{leak}}{R+ R_{leak}} \right) V_{s}= \left(\frac{10 \ k\Omega }{14.7 \ k\Omega } \right)10 \ V = 6.80 \ V[/latex]

Then,

[latex]V_{out}= \left(\frac{X_{C}}{\sqrt{R^{2}_{th}+ X^{2}_{C}} } \right)V_{th}= \left(\frac{5.0 \ k\Omega }{\sqrt{(3.2 \ k\Omega )^{2} + (5.0 \ k\Omega )^{2}} } \right)6.80 \ V= 5.73 \ V[/latex]

Question 15.26: Assume that the capacitor in Figure 15-75 is degraded to a p...

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