Question

An alternating emf E = 5.0 Sin(314 t)V is applied to a circuit containing a resistor connected in series with an unknown component X.

The current in the circuit is found to be I = `3.0 sin(314t - pi/3)A`

1. Identify the component X.
2. Calculate rms value (I_{r m s}) of the current flowing through the circuit.
3. Find the frequency of the source.
4. Calculate power factor.
5. Find the impedance (Z) of the circuit.

Answer 1

Given: E = 5.0 Sin(314 t)V

I = `3.0 sin(314t - pi/3)A`

a. Here, the current lags behind the voltage by a phase angle of `pi/3`, so the component X is an inductor.

b. I_rms = `I_0/sqrt2`

= `3/sqrt2 A`

= 2.12 A

c. Frequency of the source,

f = `W/(2 pi)`

= `314/(2 xx 3.14)`

= 50 Hz

d. Power factor cos Φ = `cos (pi/3)`

= `1/2`

= 0.5

e. Impedance (Z) = `E_0/I_0`

= `5.0/3.0`

= 1.67 Ω