You are building a small circuit that consists of a resistor in series with a ca

Question

You are building a small circuit that consists of a resistor in series with a capacitor as shown. You need the capacitor to store 23.7 mJ of energy when a 26.5V battery is connected between terminals A and B for a long time. Then, you need the capacitor to discharge half of this stored in energy in exactly 4.43 seconds when the battery is removed and replaced by a 77600 ohm load. Determine the ideal values for the capacitor and resistor such that your circuit will achieve these design goals. Show steps please.

You are building a small circuit that consists of a resistor in series with a capacitor as shown. You need the capacitor to store 23.7 mJ of energy when a 26.5 V battery is connected between terminals A and B for a long time. Then, you need the capacitor to discharge half of this stored in energy in exactly 4.43 seconds when the battery is removed and replaced by a 77600 Omega load. Determine the ideal values for the capacitor and resistor such that your circuit will achieve these design goals.

Explanation / Answer

23.7 mJ= 1/2 *C1*(26.5^2)

C1 =67.5 micro F

at half of eneryg

Vc=26.5/sqrt(2) = 18.74V = 26.5*e^(-4.43/RC1)

.3465= 4.43/RC1

RC1= 12.8

R=189kohm

R=Rl+R1

R1=112.8 Kohm

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