An ideal coil of 10 H is connected in series with a resistance of 5 Ωand a battery of 5 V .2 se

step 1 Hello students in this question we have an ideal coil of inductance L equals to 10 Henry it is c

An ideal coil of 10 H is connected in series with a...

An ideal coil of $10 \mathrm{H}$ is connected in series with a resistance of $5 \Omega$ and a battery of $5 \mathrm{~V} .2$ second after the connection is made. The current flowing in ampere in the circuit is
(A) $\left(1-e^{-1}\right)$
(B) $(1-e)$
(C) $e$
(D) $e^{-1}$

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Key Concepts

RL Circuit Analysis

This concept involves studying circuits that contain both resistors and inductors. It focuses on understanding how these circuits respond when they are subject to sudden changes, such as the closing of a switch. The analysis typically involves applying Kirchhoff's laws and solving differential equations to determine current and voltage as functions of time.

Time Constant in RL Circuits

The time constant, represented by ? = L/R, is a key parameter in RL circuits. It indicates how quickly the circuit responds to a change in voltage. A larger time constant means that the current takes longer to reach its steady state, while a smaller time constant indicates a faster response.

Transient Response and Exponential Behavior

The transient response of an RL circuit describes how the current evolves from its initial value to its final steady-state value after a switching event. This response is typically represented by an exponential function, indicating that the current gradually builds up and approaches its final value asymptotically, following the formula I(t) = I_final*(1 - e^(-t/?)).

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