Rate of change of current with time, galvanometer deflection

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A solenoid with an inductance of 2.0 H connected to a 2.0 V DC supply and a 0.5 Ω resistor will reach a final current of 4.0 A, with an initial rate of change of current of 1.0 A/s. When the current is 2.0 A, the rate of change of current is calculated to be 0.5 A/s. The discussion also covers the behavior of a secondary coil connected to a ballistic galvanometer, where a current of 4.0 A switched off in the primary solenoid results in a galvanometer deflection of 268 divisions. The importance of understanding the step response of a series R-L circuit is emphasized for solving these problems accurately.
  • #61
Bingo. Calculate the right side with numbers and you are done.
 
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  • #62
kuruman said:
Bingo. Calculate the right side with numbers and you are done.
B = μ0 n I = 4 π * 10-7 * 1000 * 4 = 5 * 10-3 T.
Q = 2000 * (8 * 10-4) * (5 * 10-3) / 60 = 1.33 * 10-4 C
 
  • #63
moenste said:
Q = Φ / R = B A N / R?
Right.
 
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  • #64
moenste said:
B = μ0 n I = 4 π * 10-7 * 1000 * 4 = 5 * 10-3 T.
Q = 2000 * (8 * 10-4) * (5 * 10-3) / 60 = 1.33 * 10-4 C
That should be 1.34*10-4..
Use sensitivity of the galvanometer to find the number of divisions.
 
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  • #65
cnh1995 said:
That should be 1.34*10-4..
Use sensitivity of the galvanometer to find the number of divisions.
θ = a Q = 2 * 1.34 * 10-4 = 2.68 * 10-4.
 
  • #66
moenste said:
θ = a Q = 2 * 1.34 * 10-4 = 2.68 * 10-4.
Well, 1.34*10-4 is the actual charge passed through the galvanometer. You have sensitivity as 2 divisions/ microcoulomb. How would you calculate the no of divisions from this?
 
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  • #67
cnh1995 said:
Well, 1.34*10-4 is the actual charge passed through the galvanometer. You have sensitivity as 2 divisions/ microcoulomb. How would you calculate the no of divisions from this?
θ = a Q = deflections of the galvanometer.

Update
1.34 * 10-4 C → 1.34 * 10-4 / 10-6 = 134 μC.

134 * 2 = 268. I think this should be right.
 
  • #68
moenste said:
θ = a Q = deflections of the galvanometer.

Update
1.34 * 10-4 C → 1.34 * 10-4 / 10-6 = 134 μC.

134 * 2 = 268. I think this should be right.
Right.
 
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