Question

The range of a galvanometer of resistance \(\mathrm{G}\) ohm is \(\mathrm{V}\) volt. The resistance required to be connected in series with it in order to convert it into voltmeter of range \(\mathrm{nV}\) volt will be (A) (G/n) (B) \(\mathrm{nG}\) (C) \((\mathrm{n}-1) \mathrm{G}\) (D) \([\mathrm{G} /(\mathrm{n}-1)]\)

Short answer

The correct answer is (C) \((n-1)G\).

Step-by-step solution

Concept of Galvanometer and Voltmeter

A galvanometer is a sensitive instrument used to measure electric current in a circuit. It has a coil of wire with a resistance G ohm and is capable of measuring current up to a certain range. A voltmeter is an instrument used to measure the potential difference (voltage) between two points in a circuit. A voltmeter's range is defined by the maximum potential difference it can measure. Step 2: Conversion from a galvanometer to a voltmeter

Converting a Galvanometer to a Voltmeter

A galvanometer can be converted into a voltmeter by connecting an additional resistance in series with it. The additional resistance, called the series resistance (S), should be chosen such that the maximum potential difference across the galvanometer corresponds to the range of the voltmeter. Since the galvanometer is measuring the voltage across its terminals, we can write that, for maximum deflection: V = I_G * G Where: - V is the range of the galvanometer in volts - I_G is the maximum current passing through the galvanometer in amperes - G is the resistance of the galvanometer in ohms Step 3: Determine the resistance required for the voltmeter

Determine the Resistance Required

Next, we need to determine the resistance required to convert the galvanometer to a voltmeter of range nV volts. For this, we use the formula for the maximum potential difference across the voltmeter (V_m): nV = I_G * (G + S) Where: - nV is the range of the voltmeter in volts - S is the series resistance in ohms Now, we can solve for S using the equations derived in step 2 and 3. Step 4: Solve the equations to find the value of S

Solve for S

From step 2: V = I_G * G From step 3: nV = I_G * (G + S) We know that I_G = V / G, so we can substitute this into the equation from step 3: nV = (V / G) * (G + S) Now, we can solve for S: nV = V + S * (V / G) S = G * (n - 1) So, the resistance required to be connected in series with the galvanometer is G * (n - 1) ohms. Looking at the answer choices, this corresponds to option C, \((n-1)G\). Therefore, the correct answer is (C) \((n-1)G\).