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Question

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with R=1000 Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?


A
The measured value of R will be 978 Ω<R<982 Ω
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B
The resistance of the ammeter will be 0.02 Ω (round off to 2nd decimal place)
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C
If the ideal cell is replaced by a cell having internal resistance of 5 Ω then the measured value of R will be more than 1000 Ω
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D
The resistance of the voltmeter will be 100 kΩ
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Solution

The correct option is B The resistance of the ammeter will be 0.02 Ω (round off to 2nd decimal place)
Given, Ig=2×106 Arg=10 Ω

For condition-I,
as a voltmeter V=ig(rg+R0) (where, R0 = shunt resistance)

reading of voltmeter =100×103
so, 100×103=2×106(10+R0)R0=50 kΩ
Hence option D is wrong.

For condition-II,
As a ammeter,

resistance of ammeter RA=G×RsG+Rs
i=ig(Rs+GRs)i=ig(rgRs)
from the given data,
1 mA=2×10610RsRs=0.02 Ω
Hence option B is correct.

For option A,

Req=980.48 ΩI=V0980.48 and V=V0×50000980.48×51

R(measured)=VI=5000051=980.4 Ω
where, The measured value of R will be 978 Ω<R<982 Ω.
Hence option A is correct.

For option C,
Internal resistance of cell will not effect for the total resistance measurment.
Hence this option is wrong.

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