Worksheet: Design of the Ohmmeter

In this worksheet, we will practice describing the combining of a galvanometer with fixed and variable resistors to design a DC ohmmeter.

Q1:

A circuit that can be used as an ohmmeter is shown. The circuit uses a galvanometer, a direct-current source with a known voltage, a fixed resistor, and a variable resistor. Which of the following most correctly states how to calibrate the circuit to directly measure the circuit’s total resistance?

  • AAdjust the resistance of the variable resistor until it is equal to the sum of the resistance of the fixed resistor and the resistance of the galvanometer.
  • BAdjust the resistance of the variable resistor until it is equal to the mean of the resistance of the fixed resistor and the resistance of the galvanometer.
  • CAdjust the resistance of the variable resistor until the galvanometer’s arm is at a full-scale deflection position.
  • DAdjust the resistance of the variable resistor until the galvanometer’s arm is at the zero-deflection position.
  • EAdjust the resistance of the variable resistor until it is equal to the difference between the resistance of the fixed resistor and the resistance of the galvanometer.

Q2:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection of the ohmmeter Φ=60. The angle of deflection of the ohmmeter arm 𝜃=30. What is the unknown resistance? Answer to the nearest .

Q3:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=48. What is the unknown resistance? Answer to the nearest kilohm.

Q4:

A circuit that can be used as an ohmmeter is shown. The circuit uses a galvanometer, a direct current source with a known voltage, a fixed resistor, and a variable resistor. The angle 𝜃 is the full-scale deflection angle of the galvanometer. Two resistors, 𝑅 and 𝑅, are connected to the ohmmeter so that their resistances can be measured by the ohmmeter. The galvanometer’s angle of deflection is reduced by the angle 𝜙 when 𝑅 is connected, and its angle of deflection is reduced by the angle 𝛼 when 𝑅 is connected; 𝛼>𝜙. Which of the following correctly relates the resistances of 𝑅 and 𝑅?

  • A𝑅<𝑅
  • B𝑅>𝑅
  • C𝑅=𝑅

Q5:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter Φ=60. The angle of deflection of the ohmmeter arm 𝜃=15. What is the unknown resistance? Answer to the nearest kilohm.

Q6:

A circuit that can be used as an ohmmeter is shown. The circuit uses a galvanometer with a resistance of 50 Ω that has a full-scale deflection current of 0.5 mA. The circuit also includes a direct current source with a voltage of 3.5 V, a fixed resistor with a resistance of 2.5 kΩ, and a variable resistor. The resistance of the variable resistor is adjusted until the galvanometer arm is at a full-scale deflection position. What resistance is the variable resistor set to? Answer to the nearest ohm.

Q7:

The diagram shows the scale of an ohmmeter that is being used to measure some unknown resistances. The resistance of the ohmmeter is 𝑅. The deflections of the ohmmeter’s arm that correspond to integer multiples of 𝑅 to the left of the direction that is halfway between zero deflection and full-scale deflection are shown, and the deflections of the ohmmeter’s arm that correspond to the reciprocals of these values are shown to the right of the direction that is halfway between zero deflection and full-scale deflection.

Which of the following most correctly describes how the deflection angles change between successive deflections that correspond to integer multiples of 𝑅 as the resistance increases above 𝑅?

  • AThe angles decrease in magnitude.
  • BThe angles have a constant magnitude.
  • CThe angles increase in magnitude.

Which of the following most correctly describes how the deflection angles change between successive deflections that correspond to the reciprocals of integer multiples of 𝑅 as the resistance decreases below 𝑅?

  • AThe angles have a constant magnitude.
  • BThe angles increase in magnitude.
  • CThe angles decrease in magnitude.

Which of the following values of resistance would an ohmmeter be showing if full-scale deflection of its arm occurred?

  • A0 Ω
  • B1𝑅 Ω
  • C Ω
  • D𝑅 Ω

Which of the following values of resistance would an ohmmeter be showing if zero deflection of its arm occurred?

  • A0 Ω
  • B𝑅 Ω
  • C Ω
  • D1𝑅 Ω

Q8:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=12. What is the unknown resistance? Answer to the nearest kilohm.

Q9:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=10. What is the unknown resistance? Answer to the nearest kilohm.

Q10:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=6. What is the unknown resistance? Answer to the nearest kilohm.

Q11:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection for the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=45. What is the unknown resistance? Answer to the nearest kilohm.

Q12:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection of the ohmmeter 𝜙=60. The angle of deflection of the ohmmeter arm 𝜃=54. What is the unknown resistance? Answer to the nearest kilohm.

Q13:

The diagram shows the scale of an ohmmeter that is being used to measure an unknown resistance. The resistance of the ohmmeter is 25 kΩ. The angle of full-scale deflection of the ohmmeter Φ=60. The angle of deflection of the ohmmeter arm 𝜃=20. What is the unknown resistance? Answer to the nearest kilohm.

Q14:

A circuit that can be used as an ohmmeter is shown. The circuit uses a galvanometer, a direct current source with a known voltage, a fixed resistor, and a variable resistor. The resistance of the variable resistor is adjusted until the galvanometer’s arm is at a full-scale deflection position. The circuit is to be used to find the resistance of a resistor that has an unknown resistance. The resistor with the unknown resistance must be connected to the circuit. In which of the following ways should the resistor be connected?

  • AIn series with all the other components
  • BIn parallel with the variable resistor
  • CIn parallel with the direct-current source
  • DIn parallel with the fixed resistor
  • EIn parallel with the galvanometer

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