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Q.

At t = 0, an inductor of zero resistance is joined to a cell of emf ‘E’ through a resistance. The current increases with a time constant $τ$ . The emf across the coil after time t is

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a

$\frac{Et}{τ}$

b

$E (1 - e^{- t / τ})$

c

${Ee}^{- \frac{t}{τ}}$

d

${Ee}^{- \frac{2 t}{τ}}$

answer is C.

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Detailed Solution

emf $E = E_{0} e^{- \frac{R}{L} t}; E = E_{0} e^{- \frac{t}{τ}} [∴ τ = \frac{L}{R}]$

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