Question 162: AC fundamentals

Question

An inductor $$(L=0.03$$ $$H)$$ and a resistor $$\left( {R = 0.15\,k\Omega } \right)$$ are connected in series to a battery of $$15V$$ $$EMF$$ in a circuit shown below. The key $${K_1}$$ has been kept closed for a long time. Then at $$t=0$$, $${K_1}$$ is opened and key $${K_2}$$  is closed simultaneously. At $$t=1$$ $$ms,$$ the current in the circuit will be : $$\left( {{e^5} \cong 150} \right)$$

Accepted Answer

$${m I}\left( 0 ight) = {{15 	imes 100} \over {0.15 	imes {{10}^3}}} = 0.1A$$
$${m I}\left( \infty  ight) = 0$$
$${m I}\left( t ight) = \left[ {{m I}\left( 0 ight) - {m I}\left( \infty  ight)} ight]\,{e^{{{ - t} \over {L/R}}}} + i\left( \infty  ight)$$
$${m I}\left( t ight) = 0.1\,{e^{{{ - t} \over {L/R}}}} = 0.1{e^{{R \over L}}}$$
$${m I}\left( t ight) = 0.1\,\,{e^{{{0.15 	imes 1000} \over {0.03}}}} = 0.67mA$$

Answer

$$6.7$$ $$mA$$

Answer

$$0.67$$ $$mA$$

Answer

$$100$$ $$mA$$

Answer

$$67$$ $$mA$$

AC fundamentals

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