Question

Explain the theory of an AC circuit with a resistor. 

Answer 1

AC circuit with resistance:

Assume an alternating emf source is applied between the terminals of a resistor with resistance R, as shown in Fig. (a). Fig

The instantaneous value of emf is given by

e = e₀ sin ωt           ...(i)

Let e be the potential drop across the resistance.

∴ e =iR                ...(ii)

But, Instantaneous emf = Instantaneous value of potential drop.

∴ From equations (i) and (ii), we have,

iR = e₀ sin ω t

`i = (e_0 sinω t)/R`          ...(iii)

We know, peak current `i_0 = e_0/R`

Substituting in equation (iii) we have,

i = i₀ sin ω t       ...(iv)

There is no phase difference between alternating current and emf according to equations (i) and (iv). In other words, there is no phase difference between current and emf.