First slide

Time -Varying current in L-R circuit

Question

Statement 1: The quantity L/R possesses dimensions of time.
Statement 2: To reduce the rate of increases of current through a solenoid, one should increase the time constant (L/R).

Moderate

A

Both statements 1 and 2 are correct
B

Statement 1 is correct statement 2 is incorrect
C

Statement 1 is incorrect statement 2 is correct
D

Both statements 1 and 2 are incorrect

Solution

The current i is given by $i = \frac{E}{R} (1 - e^{\frac{- R t}{L}}) = \frac{E}{R} (1 - e^{\frac{- t}{τ}}) \Rightarrow \frac{d i}{d t} = \frac{E}{R τ} e^{\frac{- t}{τ}}$
In order to decreases the rate of increase of current through solenoid, we have to increase the time constant $\frac{L}{R} .$
Also $\frac{L}{R} = \frac{ϕ / i}{v / i} = \frac{φ}{v} = \frac{v o l t s e c}{v o l t} = s e c$

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