Rate of change of current with time, galvanometer deflection

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SUMMARY

The discussion centers on the analysis of a solenoid with an inductance of 2.0 H connected to a 2.0 V DC supply in series with a 0.50 Ω resistor. The final current is calculated to be 4.0 A, with an initial rate of change of current at 1.0 A/s and a rate of change of 0.5 A/s when the current is 2.0 A. Additionally, the deflection of a ballistic galvanometer connected to a secondary coil of 2000 turns is determined to be 268 divisions when a primary current of 4.0 A is switched off, utilizing the formula θ = a N A B / R.

PREREQUISITES
  • Understanding of inductance and its implications in R-L circuits.
  • Familiarity with Ohm's Law and Kirchhoff's laws.
  • Knowledge of the ballistic galvanometer and its sensitivity measurements.
  • Ability to apply the formula for magnetic flux and electromagnetic induction.
NEXT STEPS
  • Study the step response of a series R-L circuit to understand current behavior over time.
  • Learn about the principles of electromagnetic induction and Faraday's law.
  • Explore the mathematical derivation of the current function i(t) in R-L circuits.
  • Investigate the operation and applications of ballistic galvanometers in measuring induced EMF.
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Students of physics, electrical engineers, and anyone interested in the dynamics of inductive circuits and electromagnetic principles.

  • #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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