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