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Standard XII

Physics

Kirchhoff's Junction Law

A coil of ind...

Question

A coil of inductance $2 H$ and resistance $10 Ω$ are in a series circuit with an open key and a cell of constant $100 V$ with negligible resistance. At time $t = 0$ , the key is closed. Find the current in the circuit at $t = 1 s$

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Solution

Given : $R = 10 Ω$ $L = 2 H$ $V = 100$ volts
Current flowing as a function of time is given by $I = \frac{V}{R} (1 - e^{- \frac{R t}{L}})$
$∴$ $I = \frac{100}{10} (1 - e^{- \frac{10 t}{2}})$
Or $I = 10 (1 - e^{- 5 t})$ $A$
Current flowing at $t = 1 s$ ,
$∴$ $I = 10 (1 - e^{- 5 \times 1})$
Or $I = 10 (1 - e^{- 5}) = 10 (1 - 6.73 \times 10^{- 3}) = 9.93 A$

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A coil of inductance 2H and resistance 10Ω are in a series circuit with an open key and a cell of constant 100V with negligible resistance. At time t=0, the key is closed. Find the current in the circuit at t=1s

Given : R=10Ω L=2 H V=100 voltsCurrent flowing as a function of time is given by I=VR(1−e−RtL)∴ I=10010(1−e−10t2)Or I=10(1−e−5t) ACurrent flowing at t=1 s,∴ I=10(1−e−5×1)Or I=10(1−e−5)=10(1−6.73×10−3)=9.93 A

A coil of inductance $2 H$ and resistance $10 Ω$ are in a series circuit with an open key and a cell of constant $100 V$ with negligible resistance. At time $t = 0$ , the key is closed. Find the current in the circuit at $t = 1 s$