Q152 / 160 · TS EAMCET 2021 (05 Aug Shift 1) · Physics

A coil of resistance $50 Ω$ is connected across a $5.0 V$ battery. If the current in the coil is found to be $50 mA$ after the time $t = 0.1 s$ battery is connected, then the inductance of the coil is

Correct answer
A
$\frac{5}{\ln (2)}$
B
$10 \ln (2)$
C
$5 e^{4}$
D
$\frac{10}{e^{4}}$

Solution

The values are given, $R = 50 Ω$ , $ε = 5 V$ , $i = 50 \times 10^{- 3} A$ and $t = 0.1 s$ , the equation of,
$i = i_{0} (1 - e^{- \frac{t \times R}{L}}) \Rightarrow 50 \times 10^{- 3} = i_{0} (1 - e^{- \frac{0.1 \times 50}{L}})$

Now use the relation between current and voltage, $i_{0} = \frac{ε}{R} = \frac{5}{50}$ ,

it means,
$\Rightarrow 50 \times 10^{- 3} = \frac{5}{50} (1 - e^{- \frac{0.1 \times 50}{L}}) \Rightarrow 50 \times 10^{- 2} = (1 - e^{- \frac{0.1 \times 50}{L}}) \Rightarrow L = \frac{5}{\ln 2}$

Hence, the correct answer is option: 'A'.

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A coil of resistance 50 Ω is connected across a 5.0 V battery. If the current in the coil is found to be 50 mA after the time t=0.1 s battery is connected, then the inductance of the coil is

Solution

Relevant Questions

A coil of resistance $50 Ω$ is connected across a $5.0 V$ battery. If the current in the coil is found to be $50 mA$ after the time $t = 0.1 s$ battery is connected, then the inductance of the coil is