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3 years ago

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A voltage v(t) = 100 cos(60t + 20°) V is applied to a parallel combination of a 40-kΩ resistor and a 50-μF capacitor. Find the s

teady-state currents through the resistor and the capacitor.

1 answer:

Misha Larkins [42]3 years ago

6 0

Answer:

Current through resistor $i_{r}=2.5cos(60t+20)mA$

Current through capacitor $i_{c}=-0.3sin(60t+20)A$

Explanation:

Given data

Voltage v(t) = 100 cos(60t + 20°) V

Resistance R=40-kΩ

Capacitor C=50-μF

To find

Steady-state currents through the resistor and the capacitor.

Solution

The current flows through the resistor is:

$i_{r}=\frac{v(t)}{R}\\ i_{r}=\frac{100cos(60t+20)}{40*10^{3} }\\ i_{r}=2.5cos(60t+20)mA$

Now the current flows through capacitor is:

$i_{c}=C\frac{dv(t)}{dt}\\ i_{c}=50*10^{-6}(\frac{d(100cos(60t+20))}{dt})\\ i_{c}=50*10^{-6}*100(-60)sin(60t+20)\\ i_{c}=-0.3sin(60t+20)A$

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