Two A.C. current i 1 & i 2 are given by i 1 = 40 sin ( 314 t + 6 π ) . i 2 = 20 sin ( 314 t − 3 π ) . Then what will be the reading of hotwire ammeter

Question

Two A.C. current i 1 ​ & i 2 ​ are given by i 1 ​ = 40 sin ( 314 t + 6 π ​ ) . i 2 ​ = 20 sin ( 314 t − 3 π ​ ) . Then what will be the reading of hotwire ammeter

TestHub · Accepted Answer

To find the hotwire ammeter reading, we need the RMS value of the resultant current.

First, find the resultant current $i = i_{1} + i_{2}$ .

$i_{1} = 40 sin (314 t + \frac{π}{6})$

$i_{2} = 20 sin (314 t - \frac{π}{3})$

The phase difference $ϕ = (\frac{π}{6}) - (- \frac{π}{3}) = \frac{π}{6} + \frac{2 π}{6} = \frac{3 π}{6} = \frac{π}{2}$ .

The peak value of the resultant current $I_{0}$ is given by:

$I_{0} = I_{01}^{2} + I_{02}^{2} + 2 I_{01} I_{02} cos ϕ$

$I_{0} = 4 0^{2} + 2 0^{2} + 2 (40) (20) cos (\frac{π}{2})$

Since $cos (\frac{π}{2}) = 0$ :

$I_{0} = 1600 + 400 + 0 = 2000 = 205 A$

The hotwire ammeter reads the RMS value of the current:

$I_{RMS} = \frac{I _{0}}{2} = \frac{20 5}{2} = 1010 A$

$I_{RMS} \approx 10 \times 3.162 = 31.62 A$

The final answer is $31.62 A$ .

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