Question

The power of a certain CD player operating at 120 V rms is 20.0 W. Assuming that the CD player behaves like a pure resistor, find (a) the maximum instantaneous power; (b) the rms current; (c) the resistance of this player.

Short answer

a) The maximum instantaneous power of the CD Player is 40 W

b) The RMS value of current is 0.167 A

c) The resistance of the CD player is 717 Ω

Step-by-step solution

concept

Resistance is a measure of opposition to the flow of current in a closed electrical circuit. It is measured in Ohm (Ω).

Root Mean Square (RMS) value is defined as the effective value of an alternating quantity. It is assumed as the equivalent steady value which will give the same effect.

given values

Power of CD Player, P_av = 20 W

Operating RMS voltage, V_rms = 120 V

Determination of Maximum Instantaneous Power

The maximum instantaneous power of an AC circuit is twice its average power:

$P_{max}=2P_{avg}=2*20=40W$

Therefore, the maximum instantaneous power of the CD Player is 40 W.

Determination of RMS Current

The RMS value of current can be found out using relation of the average power of the AC source:

$$\begin{gathered} P_{avg}=I_{rms}.V_{rms} \\ {I}_{rms}=\frac{P_{avg}}{V_{rms}} \\ =\frac{20W}{120V} \\ =0.167A \end{gathered}$$

Therefore, the RMS value of current is 0.167 A.

Determination of Capacitive reactance

The resistance of the CD player can be found out using the relation of the average power of the AC source:

$$\begin{gathered} P_{avg}={I^2}_{rms}.R \\ R=\frac{P_{avg}}{{I^2}_{rms}} \\ =\frac{20W}{{\left(0.167A\right)}^2} \\ =717\Omega \end{gathered}$$

Therefore, the resistance of the CD player is 717 Ω.