The three circuits below have driving Emf\'s with the same amplitude, 8 V. Each

Question

The three circuits below have driving Emf's with the same amplitude, 8 V. Each is driven at a fixed frequency which differs from the other two. The magnitudes of the inductive reactance in the left circuit, of the capacitive reactance in the center circuit, and of the all resistances are shown in the figures.

I. For the circuit on the left, calculate the total power dissipated.

II. For the circuit in the center, calculate the Vrms between a and b.

III. For the circuit on the right, calculate the rms current in the circuit.

Explanation / Answer

The three circuits below have driving Emf's with the same amplitude, 6 V. Each is driven at a fixed frequency which differs from the other two. The magnitudes of the inductive reactance in the left circuit, of the capacitive reactance in the center circuit, and of the all resistances are shown in the figures.

1. For the circuit on the left, calculate the total power dissipated (AVERAGE power dissipated).
2. For the circuit in the center, calculate the Vrms between a and b.
3. For the circuit on the right, calculate the rms current in the circuit.

solution:

are the voltages e1,e2, and e3 6 volts peak or RMS? I'll assume RMS
for the left circuit, the total impedance, Z = ?(13^2 +26^2) = 13?5 ohms
Only the resistor can dissipate power, P = (V^2)/R where V is the RMS voltage across the resistor R
and V = e1*R/Z so V = 6*(13/13?5) = 6/?5 volts
V^2 = 36/5
and the power is 36/((5)(13)) = 0.554 watts
(note if the voltage is peak, the power will be 1/2 of 0.554 watts since e1 rms = 6/?2, V across R= 6/?10 and V^2 = 36/10)
Middle circuit
V resistor = 6*R/Z where Z = ?(28^2 +13^2) = 30.9 ohms
V resistor = 6(13)/30.9 = 2.52 Volts
( again I have assumed e2 is 6 volts RMS, if e2 is 6 volts peak, divide 2.52 by ?2 =1.78 volts)

Last circuit
I = V/Rt where Rt = 13 +14 = 27 ohms
I = 6/27= 0.222 amps
( again I have assumed e3 is the RMS value, if e3 is 6 volts peak, the RMS voltage is 6/?2 = 4.24 volts and I rms = 4.24/27 = 0.157 amps)

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