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Ch. 26 - DC Circuits
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 26 - DC CircuitsProblem 57a
Chapter 25, Problem 57a

A galvanometer has a sensitivity of 45kΩ/V and internal resistance 20.0 Ω. How could you make this into an ammeter that reads 1.0 A full scale?

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Understand the problem: A galvanometer is a device used to measure small currents. To convert it into an ammeter that can measure larger currents (1.0 A full scale in this case), we need to add a shunt resistor in parallel with the galvanometer. This shunt resistor will bypass most of the current, allowing the galvanometer to measure only a small fraction of it.
Determine the current through the galvanometer: The galvanometer's sensitivity is given as 45 kΩ/V. This means that for every volt across the galvanometer, the current through it is I_g = V / R_g, where R_g is the internal resistance of the galvanometer (20.0 Ω). For full-scale deflection, calculate the maximum current the galvanometer can handle.
Calculate the voltage across the galvanometer: Using the maximum current the galvanometer can handle (I_g), calculate the voltage across it using Ohm's Law: V_g = I_g × R_g.
Determine the shunt resistor value: To allow the ammeter to measure up to 1.0 A, the shunt resistor (R_s) must bypass the remaining current (I_s = 1.0 A - I_g). The voltage across the shunt resistor is the same as the voltage across the galvanometer (V_g). Use Ohm's Law to find R_s: R_s = V_g / I_s.
Summarize the setup: Connect the shunt resistor (R_s) in parallel with the galvanometer. This configuration ensures that the galvanometer measures only a small fraction of the total current, while the shunt resistor carries the majority of the current, allowing the ammeter to measure up to 1.0 A full scale.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sensitivity of a Galvanometer

The sensitivity of a galvanometer refers to its ability to detect small currents, expressed in ohms per volt (Ω/V). A higher sensitivity indicates that the galvanometer can produce a larger deflection for a given current, making it more responsive. In this case, a sensitivity of 45 kΩ/V means that for every volt applied, the galvanometer can measure currents with a resistance of 45,000 ohms.

Internal Resistance

Internal resistance is the resistance within the galvanometer itself, which affects its performance when measuring current. In this scenario, the internal resistance is 20.0 Ω, which must be considered when converting the galvanometer into an ammeter. The internal resistance can lead to a voltage drop, impacting the accuracy of current readings if not properly accounted for.
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Shunt Resistor

A shunt resistor is an external resistor connected in parallel with the galvanometer to allow most of the current to bypass it. This is essential when converting a galvanometer into an ammeter, as it enables the device to measure larger currents without damaging the galvanometer. The value of the shunt resistor is calculated based on the desired full-scale current and the galvanometer's characteristics.
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Related Practice
Textbook Question

(III) Determine the net resistance in Fig. 26–61 (a) between points a and c, and (b) between points a and b. Assume R' ≠ R. [Hint: Apply an emf between the two points in each case and determine currents; use symmetry at junctions.]

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Textbook Question

(II) Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 26–63. If each internal resistance is r = 0.350Ω and R = 4.00Ω, what is the voltage across the resistor R?

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Textbook Question

(III) (a) Determine the currents I1, I2, and I3 in Fig. 26–58. Assume the internal resistance of each battery is r = 1.0 Ω.


(b) What is the terminal voltage of the 6.0-V battery?

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Textbook Question

A galvanometer has an internal resistance of 32 Ω and deflects full scale for a 48-μA current. Describe how to use this galvanometer to make a voltmeter to give a full scale deflection of 250 V.

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Textbook Question

In the circuit shown in Fig. 26–75, the 33-Ω resistor dissipates 0.80 W. What is the battery voltage?

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Textbook Question

A galvanometer has an internal resistance of 32 Ω and deflects full scale for a 48-μA current. Describe how to use this galvanometer to make an ammeter to read currents up to 25 A.

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