Question

If a coil has a resistance of 10 ohms and an inductance of 1 H, what will be the value of current 0.1 second after switching on a 500 V d.c. supply?
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Answer 1

For LR circuit , time constant τ=

R

L

=1/10=0.1s

Thus the given time t=0.1s is one time constant.

The voltage across theq

=0.37=

100

37

as P=VI

Answer 2

Step-by-step Explanation:

Given: Resistance (R) = 10 Ω

Inductance (L) = 1 H

Time (t) = 0.1 s

Voltage (V₀) for d.c. supply = 500 V

To Find: Value of current (I) after switching on d.c. supply

Solution:

• Calculating the value of current (I)

For a coil with resistance (R) and inductance (L), the value for current is calculated as;

$I = \frac{V_{0}}{R} (1-e^{-\frac{t}{\tau}})$ . . . . . . . (1)

where $\tau$ is the time constant calculated as, $\tau = \frac{R}{L}$

Therefore, $\tau = \frac{R}{L} = \frac{10}{1} = 10s$

Substituting $\tau = 10s$ and the given values in (1), we will get;

$I = \frac{500}{10} (1-e^{-\frac{0.1}{10}}) = 0.49751 \ A$

Hence, the value of current for 0.1 seconds after switching on a 500 V d.c. supply is I = 0.49751 A