Q. 95.0( 1 Vote )

# An alternating current is given by

i = i_{1} cos ωt + i_{2} sin ωt.

The rms current is given by

A. _{}

B. _{}

C. _{}

D. _{}

Answer :

The rms value of current is given by

… (i), where

i = current = i_{1} cos ωt + i_{2} sin ωt …. (ii)(given), t = time, ω = angular frequency, T = time period.

Now, squaring on both sides of (ii), we get

i^{2} = i_{1}^{2}cos^{2}ωt + 2i_{1}i_{2}sinωtcosωt + i_{2}^{2}sin^{2}ωt … (iii)

=

ow, … (v), where ω = angular frequency, T = time period = 2π/ω

Therefore, (iv) becomes:

=> [since sin nπ = 0, cos 0 = cos 2nπ = 1]

Hence, rms value of current i is (Ans)

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Consider the LCR circuit shown in Fig 7.6. Find the net current i and the phase of i. Show that . Find the impedance Z for this circuit.

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