Question

An ac-circuit having supply voltage E consists of a resistor of resistance 3W and an inductor of reactance 4W as shown in the figure. The voltage across the inductor at t p/w is

Answer 1

Answer:

     = 1.6×4 = 6.4 V

Explanation:

Here,

XL = 4 Ω

R = 3 Ω

Z = √(XL2 + R2)=√(42 + 32)

 = 5 Ω

E0 = 10 V

In the LR circuit current in the ckt is given by

I = (E0/Z)sin(ωt - Φ)

Φ = tan-1(XL/R)

=>  Φ = tan-1(4/3)

I = (E0/Z)sin(ωt - Φ)

 = (10/5) sin(ωt - Φ)

I at t = T/2

 = 2sin(ωT/2 – Φ)

=  2sin(π - Φ)

 = 2sin(tan-1(4/3))

 = 2×0.8

 = 1.6 A

Potential difference across the resistor = 1.6×R

  = 1.6×3

  = 4.8 V

Potential difference across the inductor = 1.6XL

     = 1.6×4 = 6.4 V