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Numericals · Q30

Q.A voltmeter has a resistance of 30 \Omega. What will be its reading, when it is connected across a cell of emf 2 V having internal resistance 10 \Omega?

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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A voltmeter of resistance 30 \Omega is connected directly across a cell of emf 2 V and internal resistance 10 \Omega; since the voltmeter itself completes the circuit (drawing a small current, as any real voltmeter does), the current flowing is

I=εRV+r=230+10=240=0.05 AI = \frac{\varepsilon}{R_V+r} = \frac{2}{30+10} = \frac{2}{40} = 0.05\ \text{A}

and the voltmeter reads the potential difference across its own resistance,

V=IRV=0.05×30=1.5 VV = IR_V = 0.05\times30 = 1.5\ \text{V}

which is slightly less than the cell's full 2 V emf, exactly because the voltmeter draws a small current through the cell's own internal resistance -- an explicit numerical illustration of why a real (finite-resistance) voltmeter cannot read a cell's true emf, only its loaded terminal voltage. [!ANSWER] Reading = 1.5 V

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