(a) What is the angular frequency of the circuit when R = 0? rad/s (b) What valu

Question

(a) What is the angular frequency of the circuit when R = 0?
rad/s

(b) What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in part (a)?

2.An inductor is connected to the terminals of a battery that has an emf of 12.0 V and negligible internal resistance. The current is 4.70 mA at 0.720 ms after the connection is completed. After a long time the current is 6.40 mA.

(a) What is the resistance R of the inductor?


(b) What is the inductance L of the inductor?
H

Explanation / Answer

Given that

An inductor is connected to the terminals of a battery that has an emf of (e) =12.0 V

The current is (I0) = 4.70 mA=4.70*10-3A at (t) = 0.720 ms=0.720*10-3s after the connection is completed.

After a long time the current is (If) =6.40 mA=6.40*10-3A

The resistance of the inductor is (R) give by ohms law

V =IR ===> R=V/I =12/6.40*10-3A =1875ohm

b)

We know that

i = imax (1 - e(-tR/L))

4.70 =6.40(1-e-1875ohm*0.720*10-3s/L)

0.734=1-e-1875ohm*0.720*10-3s/L

ln (0.265) =-1875ohm*0.720*10-3s/L

now the inductance L is given by L =1875ohm*0.720*10-3s/1.3280 =1.016Henry

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