Question

A) When an alternating voltage of 200 V is applied across a device X, a current of 0.4A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y, the same current again flows through the circuit, but it lags behind the applied voltage by π/2radians. Name the devices X and Y. Justify your answer.                                                                  

b) A coil of inductance 0.50H and resistance 100 Ω is connected to a 240V,50Hz AC supply. i)What is the maximum current in the coil. ii) What is the phase difference between the voltage and current?

c) The resistance in an RL circuit is 100 Ω. When the AC signal of 1000Hz is applied to the circuit, the applied voltage leads the current by 450.Calculate the inductance (L)of the coil.                              

   

Answer 1

A)

When a current is in phase with the applied voltage then it refers to that the given load is a Resistive load,

so device X is a resistor.

lags behind the applied voltage by π/2 radians, this is true for inductive circuit, therefore, device Y is a Inductor.

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B)

X_L = 2 * pi * f *L = 2 * pi * 50 * 0.50 = 157.1 ohms

so,

Z = sqrt ( R² +X_L²)

Z = 186.2 ohms

so,

I = V / Z

I = 1.288 Amps (maximum current)

and

= arctan (X_L / R)

= 57.52 degree

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C)

tan 45 = X_L / R

X_L = 100 * tan 45 = 100 ohms

so,

L = X_L / 2f

L = 15.9 mH