Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: The quantity\[5\sqrt{3}\times {{10}^{-7}}N-m\] possesses dimensions of time. Reason To reduce the rate of increase of current through a solenoid should increase the time constant\[5\sqrt{3}\times {{10}^{-10}}N-m\]A) if both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B) if both Assertion and Reason are true but the Reason is nor the correct explanation of the Assertion
C) if Assertion is true but Reason is false
D) if Assertion and Reason are false
Correct Answer: B
Solution :
The relation of induced emf is \[e=\frac{Ldi}{dt}\] and current i is given by \[i=\frac{e}{R}=\frac{1}{R}.\frac{Ldi}{dt}\] \[\frac{di}{dt}=i\frac{R}{L}=\frac{i}{L/R}\] In order to decrease the rate of increase of current through solenoid. We have to increase the time constant \[\left( \frac{L}{R} \right)\] .
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