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Standard XII

Physics

Parallel and Series Combination of Capacitors

A 3.56H ind...

Question

A $3.56 H$ inductor is placed in series with a $12.8 Ω$ resistor. An emf of $3.24 V$ is then suddenly applied across the $R L$ combination. At $0.278 s$ after the emf is applied what is the rate at which energy is being delivered by the battery?

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Solution

$τ_{L} = \frac{L}{R} = \frac{3.56}{12.8} = 0.278 s$
$i_{0} = \frac{V}{R} = \frac{3.24}{12.8} = 0.253 A$
After one time constant ( $t = 0.278 s = τ_{C}$ )
$i = (1 - \frac{1}{e}) i_{0} = 0.63 i_{0} = 0.16 A$
Power supplied by battery $= E i$
$P = (3.24 \times (0.16) = 0.518 W$

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A 3.56H inductor is placed in series with a 12.8Ω resistor. An emf of 3.24V is then suddenly applied across the RL combination. At 0.278s after the emf is applied what is the rate at which energy is being delivered by the battery?

τL=LR=3.5612.8=0.278si0=VR=3.2412.8=0.253AAfter one time constant (t=0.278s=τC)i=(1−1e)i0=0.63i0=0.16APower supplied by battery =EiP=(3.24×(0.16)=0.518W

A $3.56 H$ inductor is placed in series with a $12.8 Ω$ resistor. An emf of $3.24 V$ is then suddenly applied across the $R L$ combination. At $0.278 s$ after the emf is applied what is the rate at which energy is being delivered by the battery?

$τ_{L} = \frac{L}{R} = \frac{3.56}{12.8} = 0.278 s$
$i_{0} = \frac{V}{R} = \frac{3.24}{12.8} = 0.253 A$
After one time constant ( $t = 0.278 s = τ_{C}$ )
$i = (1 - \frac{1}{e}) i_{0} = 0.63 i_{0} = 0.16 A$
Power supplied by battery $= E i$
$P = (3.24 \times (0.16) = 0.518 W$