Question Video: Determining the Value of the Resistance of the Multiplier Resistor | Nagwa Question Video: Determining the Value of the Resistance of the Multiplier Resistor | Nagwa

Question Video: Determining the Value of the Resistance of the Multiplier Resistor Physics • Third Year of Secondary School

What is the value of the multiplier resistance required to convert a galvanometer that has a resistance of 0.2 Ω and gives full-scale deflection when a current of 2 mA passes through it to a voltmeter that measures potential difference up to 40 V?

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Video Transcript

What is the value of the multiplier resistance required to convert a galvanometer that has a resistance of 0.2 ohms and gives full-scale deflection when a current of two milliamps passes through it to a voltmeter that measures potential difference up to 40 volts? (A) 20,000.2 ohms, (B) 19,999.8 ohms, (C) 5.00005 ohms, (D) 4.99995 ohms.

In this question, we’re considering a galvanometer. And we need to find the multiplier resistance needed to convert this galvanometer to a voltmeter that measures up to a given potential difference. Let’s recall the equation that will allow us to calculate the required multiplier resistance: 𝑅 M is equal to 𝑉 max over 𝐼 G minus 𝑅 G, where 𝑅 M is the multiplier resistance. 𝑉 max is the maximum potential difference we want to measure. 𝐼 G is the current that gives the full-scale deflection on the galvanometer. And 𝑅 G is the resistance of the galvanometer.

From the question, we can see that 𝐼 G is two milliamps, 𝑅 G𝐺 is 0.2 ohms, and 𝑉 max is 40 volts. We need to convert 𝐼 G into amps. So we can recall that one milliamp is 0.001 amps, and hence two milliamps is 0.002 amps. Since we know all the quantities on the right-hand side of this equation, we can substitute them in to find the multiplier resistance. 𝑅 M is equal to 40 volts divided by 0.002 amps minus 0.2 ohms. Evaluating this expression, we find 𝑅 M to be 19,999.8 ohms. This corresponds to answer option (B).

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