### CIRCUIT THEOREM

1. With a suitable diagram show the alternating current and voltage in a pure resistance are to phase. Hence, derive an expression for power in a pure a.c resistive circuit.

1. With a suitable diagram show the alternating current and voltage in a pure resistance are to phase. Hence, derive an expression for power in a pure a.c resistive circuit.

R = resistance

From ohmâ€™s law,

V = IR

VmSinwt = IR

I =(VmsinWt) Ã· R

Recall SinWt = 1

Current(I) is maximum(IM)

IM = Vm/R

Therefore,

Instantaneous current (I) = IMSinWt

Power across the circuit, V = VMSinWt

P = IV

P = IMSinWt Ã— VMSinWt

P = VMIMSin2Wt

P =VmIM (1-cos2Wt)/2

### 2. A 60hz voltage of 180V (r.m.s) is impressed on 150â„¦ resistance. Write the time equation for the voltage across the resulting current.

F = 60hz, Vr.m.s = 180v, R = 150â„¦

W = 2Î f = 2Ã—3.142Ã—60 = 377rads/sec.

VMAX = root 2 Ã— Vr.m.s = root 2 Ã— 180 = 254.56v

Vt = VmSinwt

Vt = 254.56Sin377t

Time equation for the voltage (Vt ) = 254.56Sin377t

I(t) = It Sinwt

But, maximum current (IM) = VM/R = 254.56/150 = 1.7A\

I(t) = 1.7Sin377t

Time equation for the resulting current (It) = 1.7Sin377t Ampere