Question

An alternating voltage v=30sin50t+40cos50t is applied to a resistor of resistance 10ohm the RMS value of current through resistor is ?

Answer 1

Answer:

RMS value of the current is given as

$I_{rms} = 2.5\sqrt2$A

Explanation:

As we know that the AC voltage is given as

$V = 30 sin 50 t + 40 cos 50 t$

so here we have maximum value of voltage given as

$V_{max} = \sqrt{30^2 + 40^2}$

$V_{max} = 50 volt$

now RMS value of the voltage is given as

$V_{rms} = \frac{V_{max}}{\sqrt2}$

$V_{rms} = \frac{50}{\sqrt2}$

$V_{rms} = 25\sqrt2$

now RMS value of current can be find out by ohm's law

$I_{rms} = \frac{V_{rms}}{R}$

$I_{rms} = \frac{25\sqrt2}{10}$

$I_{rms} = 2.5\sqrt2$A

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Topic : RMS current

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