Consider the following diagram: The full scale deflection of "G" is 50 μA and the value of [math: r] is 30 Ω. Calculate the value of [math: R] if the new full scale deflection becomes 2.0 A.

Question

BlackTom AI · Accepted Answer

Voltage across the galvanometer at full deflection is Vg = Ig · r; the shunt resistor R shares the same voltage so Is · R = Ig · r, with Is = Inew − Ig.

1) Relevant concepts:
- For a galvanometer with internal resistance r and full-scale current Ig, adding a parallel shunt R to extend the range requires the same voltage across both branches.
- Conservation of current: total external current I = Ig + Is.
- Therefore R = (Ig · r)/(I − Ig).

2) Step-by-step reasoning:
- Write voltage equality: Ig·r = Is·R.
- Substitute Is = I − Ig to get R = (Ig·r)/(I − Ig).
- This formula directly gives the required shunt resistance to make the galvanometer read full scale at the larger current I.

3) Calculations (all intermediate steps shown):
- Ig = 50 μA = 50 × 10^−6 A.
- r = 30 Ω.
- I = 2.0 A.
- Compute Ig·r = (50 × 10^−6 A) × (30 Ω) = 1500 × 10^−6 V = 1.5 × 10^−3 V.
- Denominator I − Ig = 2.0 − 50 × 10^−6 = 1.99995 A.
- R = (1.5 × 10^−3) / 1.99995 ≈ 0.00075001875 Ω ≈ 0.75 × 10^−3 Ω.

4) Why the correct answer is correct:
- The shunt must carry nearly the entire 2.0 A while the galvanometer only takes 50 μA, so R must be extremely small. The derived formula and numerical substitution produce 0.75 × 10^−3 Ω, which exactly satisfies the voltage equality condition.

5) Why other options are incorrect:
- 7.5 × 10^−3 Ω is ten times too large; it would drop too much voltage and not divert enough current away from the galvanometer.
- 2.5 × 10^−3 Ω and 1.5 × 10^−3 Ω are also larger than the correct value and would not produce the required current division to give Ig = 50 μA at total 2.0 A.

6) Conclusion:
The computed shunt resistance is R ≈ 0.75 × 10^−3 Ω, confirming the provided correct answer.

Consider the following diagram: The full scale deflection of "G" is 50 μA and the value of [math: r] is 30 Ω. Calculate the value of [math: R] if the new full scale deflection becomes 2.0 A.单项选择题

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