Question

A sinusoidal voltage of frequency 60Hz and peak value 150V is applied to a series L-R circuit, where R=20Omega and L=40mH (a) compute T, omega, X_L, Z and phi (b) Compute the amplitudes of current V_R and V_L

Answer 1

Given:

Sinusoidal wave  frequency 60 hertz

peak value = 150V

R=20ohms

L = 40mH

To find:

1)T    2)w 3)$X_{L}$ 4)Z 5)phase angle

Solution:

let the sin wave is $V_{0$sin(wt+Ф)

$V_{0 = 150V$

T = 1/F= 1/60seconds

w = 2πF = 2×3.14×60 = 376.8rad/sec

$X_{L}$ = wL

    = 376.8×40 ×$10^{-3}$

$X_{L}$ = 15.072ohms

Z = $\sqrt{X_{L} ^{2} + R^{2} }$

Z= 25.04ohms

cosФ = $\frac{R}{Z}$

Ф = 37.8

since the circuit is inductive voltage is ahead of current by a phase angle Ф.

I = $I_{0}$sin(wt -Ф)

$I_{0} = \frac{V_{0} }{Z}$

    = $\frac{150}{Z}$

   =6 amps

$V_{R0}$ = $I_{0}$×R

    6×20 =120 volts

$V_{L0} = I_{0} X_{L}$

     6×15.072

    ≈ 91 volts

     

1)T = 1/60 secs.  2) w= 376.8rads/sec  3) $X_{L}$ = 15.07ohms

4) Z = 25.04 ohms   5) 37.8   6)I = 6 amps

7) $V_{R0}$=120 volts

8) $V_{L0} = 91 volts$