An ac current is represented as The r.m.s. value of the current is [2025]

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Solution

Q.
An ac current is represented as

$i = 5 \sqrt{2} + 10 \cos (650 π t + \frac{π}{6}) Amp$

The r.m.s. value of the current is [2025]

1 20 Amp

2 100 Amp

3 10 Amp

4 $5 \sqrt{2} Amp$

Ans.
(3)

$i = 5 \sqrt{2} + 10 \cos (650 π t + \frac{π}{6})$

$i^{2} = 50 + 100 \cos^{2} (650 π t + \frac{π}{6})$ $+ (2) (5 \sqrt{2}) (10) \cos (650 π t + \frac{π}{6})$

$< i^{2} > = 50 + \frac{100}{2} + 0$

$< i^{2} > = 100$

$< i > = 10 Amp$

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