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Specify the points to which you could connect a voltmeter to measure the following potential differences in [link] : (a) the potential difference of the voltage source; (b) the potential difference across R 1 size 12{R rSub { size 8{1} } } {} ; (c) across R 2 size 12{R rSub { size 8{2} } } {} ; (d) across R 3 size 12{R rSub { size 8{3} } } {} ; (e) across R 2 size 12{R rSub { size 8{2} } } {} and R 3 size 12{R rSub { size 8{3} } } {} . Note that there may be more than one answer to each part.

This figure shows a circuit having a cell of e m f script E and internal resistance r connected in parallel to two arms, one arm containing resistor R sub one and a second arm containing a series of resistors R sub two and R sub three.
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To measure currents in [link] , you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following: (a) the total current; (b) the current flowing through R 1 size 12{R rSub { size 8{1} } } {} ; (c) through R 2 size 12{R rSub { size 8{2} } } {} ; (d) through R 3 size 12{R rSub { size 8{3} } } {} . Note that there may be more than one answer to each part.

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Problem exercises

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 size 12{1 "." "00""-M" %OMEGA } {} resistance on its 30.0-V scale?

30 μA size 12{"30" μA} {}

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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 size 12{"25" "." 0"-k" %OMEGA } {} resistance on its 100-V scale?

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Find the resistance that must be placed in series with a 25 . 0-Ω size 12{"25" "." 0- %OMEGA } {} galvanometer having a 50.0 -μA size 12{"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.

1 . 98 k Ω size 12{1 "." "98 k" %OMEGA } {}

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Find the resistance that must be placed in series with a 25 . 0-Ω size 12{"25" "." 0- %OMEGA } {} galvanometer having a 50 . 0-μA size 12{"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.

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Find the resistance that must be placed in parallel with a 25 . 0-Ω size 12{"25" "." 0- %OMEGA } {} galvanometer having a 50 . 0-μA size 12{"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.

1 . 25 × 10 - 4 Ω size 12{1 "." "25"´"10" rSup { size 8{ +- 4} } %OMEGA } {}
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Find the resistance that must be placed in parallel with a 25 . 0-Ω size 12{"25" "." 0- %OMEGA } {} galvanometer having a 50 . 0-μA size 12{"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.

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Find the resistance that must be placed in series with a 10 . 0-Ω size 12{"10" "." 0- %OMEGA } {} galvanometer having a 100-μA size 12{"100"-μA} {} sensitivity to allow it to be used as a voltmeter with: (a) a 300-V full-scale reading, and (b) a 0.300-V full-scale reading.

(a) 3 . 00 M Ω size 12{3 "." "00 M" %OMEGA } {}

(b) 2 . 99 k Ω size 12{2 "." "99 k" %OMEGA } {}

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Find the resistance that must be placed in parallel with a 10 . 0-Ω size 12{"10" "." 0- %OMEGA } {} galvanometer having a 100-μA size 12{"100"-μA} {} sensitivity to allow it to be used as an ammeter with: (a) a 20.0-A full-scale reading, and (b) a 100-mA full-scale reading.

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Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of 0 . 100 Ω size 12{0 "." "100" %OMEGA } {} by placing a 1 . 00 -k Ω size 12{1 "." "00""-k" %OMEGA } {} voltmeter across its terminals. (See [link] .) (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

The figure shows a circuit diagram that includes a battery with an internal resistance r and a voltmeter connected across its terminals. The current I is shown by an arrow pointing in a clockwise direction.

(a) 1.58 mA

(b) 1.5848 V (need four digits to see the difference)

(c) 0.99990 (need five digits to see the difference from unity)

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Suppose you measure the terminal voltage of a 3.200-V lithium cell having an internal resistance of 5 . 00 Ω size 12{5 "." "00" %OMEGA } {} by placing a 1 . 00 -k Ω size 12{1 "." "00""-k" %OMEGA } {} voltmeter across its terminals. (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

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A certain ammeter has a resistance of 5 . 00 × 10 5 Ω size 12{5 "." "00"´"10" rSup { size 8{-5} } %OMEGA } {} on its 3.00-A scale and contains a 10 . 0-Ω size 12{"10" "." 0- %OMEGA } {} galvanometer. What is the sensitivity of the galvanometer?

15 . 0 μA size 12{"15" "." 0 mA} {}

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A 1 . 00 -MΩ size 12{1 "." "00""-M" %OMEGA } {} voltmeter is placed in parallel with a 75 . 0 -k Ω size 12{"75" "." 0"-k" %OMEGA } {} resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) What is the resistance of the combination? (c) If the voltage across the combination is kept the same as it was across the 75 . 0 -k Ω size 12{"75" "." 0"-k" %OMEGA } {} resistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the 75 . 0 -k Ω size 12{"75" "." 0"-k" %OMEGA } {} resistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

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A 0 . 0200-Ω ammeter is placed in series with a 10 . 00-Ω size 12{"10" "." "00"- %OMEGA } {} resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the 10 . 00-Ω size 12{"10" "." "00"- %OMEGA } {} resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the 10 . 00-Ω size 12{"10" "." "00"- %OMEGA } {} resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

(a)

The figure shows part of a circuit that includes an ammeter with internal resistance r connected in series with a load resistance R.

(b) 10 . 02 Ω size 12{10 "." "02 " %OMEGA } {}

(c) 0.9980, or a 2.0 × 10 –1 percent decrease

(d) 1.002, or a 2.0 × 10 –1 percent increase

(e) Not significant.

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Unreasonable Results

Suppose you have a 40 . 0-Ω size 12{"40" "." 0- %OMEGA } {} galvanometer with a 25 . 0-μA size 12{"25" "." 0-mA} {} sensitivity. (a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for 0.500 mV? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

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Unreasonable Results

(a) What resistance would you put in parallel with a 40 . 0-Ω size 12{"40" "." 0- %OMEGA } {} galvanometer having a 25. 0-μA sensitivity to allow it to be used as an ammeter that has a full-scale deflection for 10 . 0-μA size 12{"10" "." 0 μA} {} ? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) 66 . 7 Ω size 12{-"66" "." 7 %OMEGA } {}

(b) You can’t have negative resistance.

(c) It is unreasonable that I G size 12{I rSub { size 8{G} } } {} is greater than I tot size 12{I rSub { size 8{"tot"} } } {} (see [link] ). You cannot achieve a full-scale deflection using a current less than the sensitivity of the galvanometer.

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Questions & Answers

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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