# Circuits and DC Instruments

Lead Author(s): **Openstax Content**

Source: **OpenStax**

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This pack examines resistors in series/parallel, terminal voltage, Kirchoff's Rules, DC Voltmeters, null measurements and more.

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Your car's 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.) (answer in W)

Standard automobile batteries have six lead-acid cells in series, creating a total emf of 12.0 V. What is the emf of an individual lead-acid cell? (answer in V)

What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell’s internal resistance is 2.00 Ω ? (answer in V)

What is the internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 15.0 V while a current of 8.00 A is charging it? (answer in Ω)

Electric fish generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. Each electroplaque has an emf of 0.15 V and internal resistance of 0.25 Ω. If the water surrounding the fish has resistance of 800 Ω, how much current can the eel produce in water from near its head to near its tail? (answer in A)

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 1.00-M Ω resistance on its 30.0-V scale? (answer in μA)

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 25.0-k Ω resistance on its 100-V scale? (answer in mA)

Find the resistance that must be placed in series with a 25.0-Ω galvanometer having a 50.0-µA sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 0.100-V full-scale reading. (answer in kΩ)

Find the resistance that must be placed in series with a 25.0-Ω galvanometer having a 50.0-µA sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 3000-V full-scale reading. Include a circuit diagram with your solution. (answer in ×10$^{7}$ Ω)

Find the resistance that must be placed in parallel with a 25.0-Ω galvanometer having a 50.0-µA sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 10.0-A full-scale reading. Include a circuit diagram with your solution. (answer in ×10$^{-4}$ Ω)

Find the resistance that must be placed in parallel with a 25.0-Ω galvanometer having a 50.0-µA sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 300-mA full-scale reading. (answer in ×10$^{-3}$ Ω)

A certain ammeter has a resistance of 5.00×10$^{-5}$ Ω on its 3.00-A scale and contains a 10.0-Ω galvanometer. What is the sensitivity of the galvanometer? (answer in μA)

What is the emfx of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 V and the potentiometer balances for *R*$_{x}$ = 5.000 Ω and r s = 2.500 Ω ? (answer in V)

Calculate the emfx of a dry cell for which a potentiometer is balanced when *R*$_{x}$ = 1.200 Ω, while an alkaline standard cell with an emf of 1.600 V requires r s = 1.247 Ω to balance the potentiometer. (answer in V)

When an unknown resistance *R*$_{x}$ is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting *R*$_{3}$ to be 2500 Ω . What is *R*$_{x}$ if $R_{2} \over R_{1}$ = 0.625? (answer in kΩ)

To what value must you adjust *R*$_{3}$ to balance a Wheatstone bridge, if the unknown resistance *R*$_{x}$ is 100 Ω, *R*$_{1}$ is 50.0 Ω, and *R*$_{2}$ is 175 Ω ? (answer in Ω)

A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance? (answer in ×10$^{7}$ Ω)

After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor C, charged through a resistance *R*? (answer in %)

Using the exact exponential treatment, find how much time is required to discharge a 250-µF capacitor through a 500-Ω resistor down to 1.00% of its original voltage. (answer in s)

Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-M Ω resistor to 90.0% of its final voltage. (answer in ×10$^{-2}$ s)

**Integrated concepts**
If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an *RC* discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one *RC* constant is acceptable, and given that the flash is driven by a 600-µF capacitor, what is the resistance in the flash tube? (answer in ×10$^{-3}$ Ω)

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