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Q52PE

Expert-verifiedFound in: Page 777

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**A certain ammeter has a resistance of \(5.00 \times {10^{ - 5}}{\rm{ }}\Omega \) on its \(3.00 - A\) scale and contains a \(10.0 - \Omega \) galvanometer. What is the sensitivity of the galvanometer?**

The galvanometer inside an ammeter with internal resistance \(r = 10{\rm{ }}\Omega \) has a sensitivity value of \({I_g} = 15{\rm{ }}\mu A\).

**A galvanometer is an electromechanical device used to detect electric current. A galvanometer deflects a pointer in response to an electric current flowing through a coil in a constant magnetic field. An example of an actuator is a galvanometer.**

**The total flow of electrons via a wire can be used to describe the rate of electron flow. Anything that prevents current flow is referred to as "resistance." An electrical circuit needs resistance in order to transform electrical energy into light, heat, or movement.**

- An ammeter with resistance: \(R = 5 \cdot {10^{ - 5}}{\rm{ }}\Omega \)
- An ammeter with a scale: \({I_{tot}} = 3{\rm{ }}A\)
- A galvanometer with internal resistance: \(r = 10{\rm{ }}\Omega \)

The sensitivity of the galvanometer is the current that goes through the galvanometer\({I_g}\). Obtain the sensitivity by noting that \(R\) and \(r\) are at same potentials, which gives –

\(\begin{align}{c}{I_g}r & = {I_R}R\\{I_g}r & = \left( {{I_{tot}} - {I_g}} \right)R\\{I_g}(r + R) & = {I_{tot}}R\\{I_g} & = \frac{R}{{r + R}}{I_{tot}}\end{align}\)

\(\begin{align}{} & = \frac{{5\cot {{10}^{ - 5}}{\rm{ }}\Omega }}{{\left( {10 + 5 \cdot {{10}^{ - 5}}} \right)\Omega }}(3\;A)\\ & = 1.5 \cdot {10^{ - 5}}\;A\\ &= 15{\rm{ }}\mu A\end{align}\)

Therefore, the value of the current is obtained as \({I_g} = 15{\rm{ }}\mu A\).

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