A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply. (a) What is the maximum current in the coil? (b) What is the time lag between the voltage maximum and the current maximum?

Inductance of the inductor, L = 0.50 H

Resistance of the resistor, R = 100Ω.

Potential of the supply voltage, V = 240 V

Frequency of the supply, v = 50 Hz

Ans (a).

Peak voltage is given as: V₀ = √2 V

= √2 x 240= 339.41 V

Angular frequency of the supply, ω = 2πν = 2π x 50 = 100π rad/s

Maximum current in the circuit is given as:

I₀ = V₀ /√ (R² + ω² L²) =339.41/√[ (100)² + (100π)² (0.50)²

=1.82 A

Ans (b).

Equation for voltage is given as : V= V₀ cosωt

Equation for current is given as ;I = I₀ cos(ωt-φ )

Where,φ = Phase difference between voltage and current .At time t=0

V= V₀(voltage is maximum)

Hence, the time lag between maximum voltage and maximum current is φ/ω

Now, phase angle φ is given by the relation,

tan φ = ωL/R

=(2π x 50 x 0.5)/100=1.57

=>φ= 57.5º = 57.5 π/180 rad

=>ωt =57.5 π/180

=>t = 57.5 /(180 x 2π x50)= 3.19 x 10⁻³ s = 3.2ms

Hence ,the time lag between maximum voltage and maximum current is 3.2 ms