Question 88: Current Electricity

Question

Two identical moving coil galvanometers have 10$$\Omega $$ resistance and full scale deflection at 2$$\mu $$A 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$$\Omega $$ resistor by using an ideal cell. Which of the following statement(s) is/are correct?

Accepted Answer

$$V = 100 	imes {10^{ - 3}} = {10^{ - 1}}V$$
$$V = {{\mathop{m l}
olimits} _g}({R_g} + {R_v})$$
$${{{{10}^{ - 1}}} \over {2 	imes {{10}^{ - 6}}}}={R_g} + {R_v}$$
$$5 	imes {10^4}\Omega  \approx {R_v}$$ ($$ \because $$$${R_v} < {10^5}\Omega $$)
I
g
R
g
= (I - I
g
)S
$$S = {{2 	imes {{10}^{ - 6}} 	imes 10} \over {{{10}^{ - 3}} - 2 	imes {{10}^{ - 6}}}}$$
$$S = 2 	imes {10^{ - 5}} 	imes {10^3} = 2 	imes {10^{ - 2}} = 20m\Omega $$
$${R_A} = {{S{R_g}} \over {S + {R_g}}} = {{20 	imes {{10}^{ - 3}} 	imes 10} \over {10 + 20 	imes {{10}^{ - 3}}}}$$
$$ \approx 20 	imes {10^{ - 3}}\Omega $$
$$i = {\varepsilon  \over {\left( {{{1000 	imes 50 	imes {{10}^3}} \over {51 	imes {{10}^3}}}} ight)}} = {{51\varepsilon } \over {5 	imes {{10}^4}}}$$
($$ \because $$ R
A
$$ 	o $$ 0)
$$i' = i\left( {{{{R_v}} \over {51 	imes {{10}^3}}}} ight) = {\varepsilon  \over {1000}}$$
Measured resistance,
$$ 	herefore $$ $${R_m} = {{i' 	imes 1000} \over i} = {\varepsilon  \over {51\varepsilon }} 	imes 5 	imes 10 = 980.4\Omega $$
If the voltmeter shows full scale deflection then
$${\varepsilon  \over {980}} 	imes \left( {{{1000} \over {51 	imes {{10}^3}}}} ight) 	imes 5 	imes {10^4} = {10^{ - 1}}$$
$$\varepsilon  = 999.6$$ mV
Since, i
A
= 1 mA so maximum reading of R can be
$${{999.6\,mV} \over {1\,mA}} = 999.6\Omega $$

Answer

The resistance of the voltmeter will be 100 k$$\Omega $$.

Answer

The resistance of the ammeter will be 0.02 $$\Omega $$(round off to 2nd decimal place).

Answer

If the ideal cell is replaced by a cell having internal resistance of 5$$\Omega $$ then the measured value of R will be more than 1000$$\Omega $$.

Answer

The measured value of R will be 978$$\Omega $$ < R < 982$$\Omega $$.

Current Electricity

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