A direct voltage of 200 V is suddenly applied to a series RL circuit having R - 20- and L- 0-2 H- The rate of change of current at t- 0-02 sec is A-sec-

As the voltage is applied suddenly The current in the circuit i(t) = I_∞ (I_∞ I_0)e^ t/τ time constant,τ=LR=0.220=0.01s i(t)=10 10 e^ 100t didt=1000 e^ 100t ...

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Circuit Theory

RL transients-2

A direct volt...

Question

A direct voltage of 200 V is suddenly applied to a series RL circuit having $R = 20 Ω$ and $L = 0.2 H$ . The rate of change of current at $t = 0.02 s e c$ is______ A/sec.

112.67

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154.65

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135.33

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56.9

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Solution

The correct option is C 135.33
As the voltage is applied suddenly
The current in the circuit
$i (t) = I_{\infty} - (I_{\infty} - I_{0}) e^{- t / τ}$

time constant, $τ = \frac{L}{R} = \frac{0.2}{20} = 0.01 s$

$i (t) = 10 - 10 e^{- 100 t}$

$\frac{d i}{d t} = 1000 e^{- 100 t}$

${\begin{matrix} \frac{d i}{d t} \end{matrix} ∣ ∣ ∣}_{t = 0.02 s} = 1000 e^{- 100 \times 0.02}$

${\begin{matrix} \frac{d i}{d t} \end{matrix} ∣ ∣ ∣}_{t = 0.02 s} = 135.33 A / s$

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A direct voltage of 200 V is suddenly applied to a series RL circuit having R=20Ω and L=0.2H. The rate of change of current at t=0.02sec is______ A/sec.

The correct option is C 135.33As the voltage is applied suddenly The current in the circuit i(t)=I∞−(I∞−I0)e−t/τ time constant,τ=LR=0.220=0.01s i(t)=10−10e−100t didt=1000e−100t didt∣∣∣t=0.02s=1000e−100×0.02 didt∣∣∣t=0.02s=135.33A/s

A direct voltage of 200 V is suddenly applied to a series RL circuit having $R = 20 Ω$ and $L = 0.2 H$ . The rate of change of current at $t = 0.02 s e c$ is______ A/sec.