Electronic devices often use an RC circuit, as shown in the figure below, to pro

Question

Electronic devices often use an RC circuit, as shown in the figure below, to protect against power outages, for this case, the capacitance is 14 muF.

(a) Calculate the maximum and minimum currents that can flow through the circuit. state under what specific conditions each one occurs (for example: during charging or after the capacitor is fully charged, when the capacitor is fully discharged and will start to charge, etc.)

(b) If the device is supposed to keep the supply voltage at least 70 percent of its maximum value for as long 0.20s, find the value of the resistor.

(c)Between which two terminals should the electronic device be connected: and b, b and c, or a and c? justify your answer.

Explanation / Answer

(a) Normally there is no DC current in the circuit, so the voltage of the battery is across the capacitor.

When there is an interruption, the capacitor voltage will decrease exponentially: VC = V0 e ^– t/ .

We find the time constant from the need to maintain 70% of the voltage for 0.20 s: 0.70V0 = V0 e^ – (0.20 s)/ ,

or (0.20 s)/ = ln(1.43) = 3.57, which gives = 0.56 s.

We find the required resistance from = RC; 0.56 s = R(22 × 10–6 F), which gives R = 2.5 × 104 = 25 k.

(b) In normal operation, there will be no voltage across the resistor, so the device should be connected between b and c.

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