JEE Advanced · PhysicsMedium

$An AC voltage source V = 200 sin (100 t) V is applied across a parallel combination of a resistor R = 100 Ω and an inductor L = 1 H . The total current drawn from the source is:$

A. $2 sin (100 t) + 2 cos (100 t) A$
B. $2 sin (100 t) - 2 cos (100 t) A$
C. $2 sin (100 t) + 200 cos (100 t) A$
D. $200 sin (100 t) - 2 cos (100 t) A$

Show correct answer & step-by-step solution

Correct answer: B — $2 sin (100 t) - 2 cos (100 t) A$

Solution

$Current through resistor I_{R} = V / R = (200 sin (100 t)) /100 = 2 sin (100 t) .$
$Current through inductor I_{L} = \int (V / L) d t = \int (200 sin (100 t) /1) d t = - 2 cos (100 t) .$
$Total current I = I_{R} + I_{L} = 2 sin (100 t) - 2 cos (100 t) .$
$Hence the answer is (B).$

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