Question

54. the current in the rl circuit shown here increases to 40% of its steady-state value in 2.0 s. what is the time constant of the circuit?

Answer 1

The time constant of the circuit is 3.92s.

In a circuit, what is RL?

A type of circuit known as an RL Circuit (resistor-inductor circuit), also known as an RL Network or an RL Filter, consists of a pair of inductors and resistors and is typically powered by an external source. As a result, an RL circuit consists of an inductor and a resistor connected in either series or parallel fashion.

During charging, the expression of current through the resistor in the RL-circuit shows that

I(t) = I₀ (1-$e^{1/t}$)

10=4(1-0²)

Here I₀ is maximum current through resistor,τis time constant and t is time.

Time constant of the circuit is calculated as follows,

Substitute 0.40I₀, for I (t) and 2.0 s for t in above current equation,

0.40I₀= I₀ (1-$e^{-2.0x/r}$)

0.40 = 1-$e^{-2.0x/r}$

$e^{-2.0x/r}$ = 0.60

Take natural log both side

-2.0 s/τ = In (0.60)

-2.0 s/τ = -0.51

τ = 3.92 s

Hence time constant of the circuit is 3.92s.

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