Current Electricity 5 Question 3

3. The actual value of resistance R, shown in the figure is 30Ω. This is measured in an experiment as shown using the standard formula R=VI, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5 less, then the internal resistance of the voltmeter is

(2019 Main, 10 Jan II))

(a) 600Ω

(b) 570Ω

(c) 350Ω

(d) 35Ω

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Solution:

  1. Measured value of R=5 less than actual value of R.

Actual values of R=30Ω

So, measured value of R is

R=30(5R=28.5Ω

Now, let us assume that internal resistance of voltmeter RV. Replacing voltmeter with its internal resistance, we get following circuit.

It is clear that the measured value, R should be equal to parallel combination of R and RV. Mathematically,

R=RRVR+RV=28.5Ω Given, R=30Ω30RV30+RV=28.530RV=(28.5×30)+28.5RV1.5RV=28.5×30RV=28.5×301.5=19×30 or RV=570Ω



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