Worksheet: Design of the Voltmeter

In this worksheet, we will practice describing the combining of a galvanometer with a multiplier resistor to design a DC voltmeter.

Q1:

Which of the following is the most correct description of how the range of values of voltages that a galvanometer being used as a voltmeter can produce can be extended when a multiplier resistor is used?

  • AA multiplier resistor with a resistance much greater than that of the galvanometer is connected in parallel with the galvanometer.
  • BA multiplier resistor with a resistance equal to that of the galvanometer is connected in series with the galvanometer.
  • CA multiplier resistor with a resistance much greater than that of the galvanometer is connected in series with the galvanometer.
  • DA multiplier resistor with a resistance much smaller than that of the galvanometer is connected in series with the galvanometer.
  • EA multiplier resistor with a resistance much smaller than that of the galvanometer is connected in parallel with the galvanometer.

Q2:

A voltmeter is used to measure the voltage of a direct-current source that is estimated to have a voltage of several volts. The galvanometer in the voltmeter has a resistance of a few milliohms. Which of the following correctly explains why the multiplier resistor in such a voltmeter must have a resistance much greater than the resistance of the galvanometer that the multiplier is connected in series with?

  • AIf the multiplier resistor has a resistance of a magnitude comparable with or less than that of the galvanometer, the current through the galvanometer will be greater than the current that would produce a full-scale deflection of the galvanometer arm.
  • BIf the multiplier resistor has a resistance of a magnitude comparable with or less than that of the galvanometer, the resistor will generate a magnetic field that significantly changes the deflection of the galvanometer arm.
  • CIf the multiplier resistor has a resistance of a magnitude comparable with or less than that of the galvanometer, the voltage of the source will be significantly increased.
  • DIf the multiplier resistor has a resistance of a magnitude comparable with or less than that of the galvanometer, the direction of the deflection of the galvanometer arm will reverse and no reading will be displayed on the voltmeter.

Q3:

The voltage 𝑉 in the circuit shown is 12 V, which is the greatest voltage that can be measured using the circuit as a voltmeter. The resistance of the galvanometer is one-hundredth of the resistance of the shunt.

Find 𝑉, the voltage across the galvanometer. Answer to the nearest millivolt.

Find 𝑉, the voltage across the multiplier. Answer to one decimal place.

Q4:

Which of the following circuit diagrams most correctly represents a galvanometer combined with a multiplier resistor being used as a voltmeter to measure the voltage of a direct-current source?

  • A
  • B
  • C

Q5:

The diagram shows a galvanometer that has two scales. One of the scales is a galvanometer scale and the other scale is a voltmeter scale. The galvanometer is part of a circuit that contains a multiplier resistor. When a current is measured, the galvanometer arm deflects so that it points at the position indicating the maximum magnitude of current on the galvanometer scale, and this value is 𝑋 μA. The voltmeter scale reads a value of 𝑌 mV. Which of the following statements is true?

  • AThe ratio depends only on the resistance of the galvanometer.
  • BThe ratio of 𝑋 to 𝑌 is 2.
  • CThe ratio of 𝑋 to 𝑌 is 1.
  • DThe ratio depends only on the resistance of the multiplier resistor used.
  • EThe ratio depends on the resistance of the multiplier resistor used and the resistance of the galvanometer.

Q6:

The circuit diagram represents a galvanometer combined with a multiplier resistor. The multiplier resistor has a resistance fifty times that of the galvanometer. What is the ratio of the current in the galvanometer, 𝐼G, to the current in the multiplier resistor, 𝐼M?

Q7:

A galvanometer has a resistance of 12 mΩ. A multiplier resistor is connected in series with the galvanometer to convert it into a voltmeter. The resistance of the multiplier is 1.1 kΩ. What percent of the greatest voltage that the voltmeter can measure is the voltage across the galvanometer? Answer to four decimal places.

Q8:

A galvanometer has a resistance of 175 mΩ. A current of 20 mA produces a full-scale deflection of the galvanometer. Find the resistance of a multiplier resistor that, when connected in series with the galvanometer, allows it to be used as a voltmeter that can measure a maximum voltage of 15 V. Answer to the nearest ohm.

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