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A galvanometer is to be converted into a...

A galvanometer is to be converted into an ammeter or voltmeter. In which of the following cases the resistance of the device is largest?

A

An ammeter of range 10 A

B

A voltmeter of range 5 V

C

An ammeter of range 5A

D

A voltmeter of range 10 V.

Text Solution

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The correct Answer is:
To determine in which case the resistance of the device is largest when converting a galvanometer into an ammeter or voltmeter, we can follow these steps: ### Step 1: Understand the Conversion of Galvanometer to Ammeter - When converting a galvanometer to an ammeter, a shunt resistor (S) is connected in parallel with the galvanometer (Rg). - The purpose of the shunt is to allow most of the current to bypass the galvanometer, thus protecting it from high currents. ### Step 2: Analyze the Resistance in Ammeter Configuration - The equivalent resistance (R_eq) of the ammeter configuration is given by the formula for resistors in parallel: \[ \frac{1}{R_{eq}} = \frac{1}{R_g} + \frac{1}{S} \] - Since S is much smaller than Rg, R_eq will be relatively low. This means that the ammeter has a low resistance. ### Step 3: Understand the Conversion of Galvanometer to Voltmeter - When converting a galvanometer to a voltmeter, a series resistor (R) is connected in series with the galvanometer. - This series resistor is often referred to as the multiplier resistance. ### Step 4: Analyze the Resistance in Voltmeter Configuration - The equivalent resistance (R_eq) of the voltmeter configuration is simply the sum of the resistances: \[ R_{eq} = R_g + R \] - Since both resistances are in series, R_eq will be relatively high. This means that the voltmeter has a high resistance. ### Step 5: Compare the Resistances - From the analysis: - The resistance of the ammeter (R_eq for ammeter) is low due to the parallel configuration. - The resistance of the voltmeter (R_eq for voltmeter) is high due to the series configuration. ### Step 6: Conclusion - Therefore, the resistance of the device is largest when the galvanometer is converted into a voltmeter. ### Final Answer The resistance of the device is largest when the galvanometer is converted into a voltmeter.
To determine in which case the resistance of the device is largest when converting a galvanometer into an ammeter or voltmeter, we can follow these steps: ### Step 1: Understand the Conversion of Galvanometer to Ammeter - When converting a galvanometer to an ammeter, a shunt resistor (S) is connected in parallel with the galvanometer (Rg). - The purpose of the shunt is to allow most of the current to bypass the galvanometer, thus protecting it from high currents. ### Step 2: Analyze the Resistance in Ammeter Configuration - The equivalent resistance (R_eq) of the ammeter configuration is given by the formula for resistors in parallel: ...
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