The three circuits below have driving Emf\'s with the same amplitude, 9 V. Each

Question

The three circuits below have driving Emf's with the same amplitude, 9 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 rms current in the circuit.

II. For the circuit in the center, calculate the total power dissipated.

III. For the circuit on the right, calculate the Vrms between a and b.

Explanation / Answer

i) Impedence of the ckt, z = sqrt(R^2 + XL^2)

= sqrt(17^2 + 21^2)

= 27 ohms

I_peak = V_peak/z

= 9/27

= 0.3333 A

I_rms = I_peak/sqrt(2)

= 0.3333/sqrt(2)

= 0.256 A

ii) Impedence of the ckt, z = sqrt(R^2 + Xc^2)

= sqrt(17^2 + 24^2)

= 29.41 ohms

I_peak = V_peak/z

= 9/29.41

= 0.306 A

I_rms = I_peak/sqrt(2)

= 0.306/sqrt(2)

= 0.216 A

Vrms(ab) = Irms*R

= 0.216*17

= 3.68 volts

iii) Average power dissipated = V^2/(2*Rnet)

= 9^2/(2*(14+17))

= 1.306 Watts

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