Question

A moving coil instrument whose resistance is $25\Omega$ given a full-scale deflection with a voltage of 25 mV. The instrument is to be used with a series multiplier to extend its range to 10 V. Then the error caused by ${10}^{\circ }C$ rise in temperature is (The temperature coefficient of copper is $0.004\Omega /{\Omega }^{\circ }C$ and that of margin $0.00015\Omega /{\Omega }^{\circ }C$)

• A. 0.16% low
• B. 0.16% fast
• C. 0.24% low
• D. 0.24% fast

Answer 1

The correct option is A 0.16% low

Meter current for full scale deflection,

$I_m=\frac{V}{R_m}=\frac{25\times {10}^{-3}}{25}=1mA$

Voltage multiplying factor,
$m=\frac{V}{v}=\frac{10}{25\times {10}^{-3}}=400$

Multiplier resistance,
$R_s=(m-1)R_m$
$=(400-1)\times 25=9975\Omega$

Total resistance of voltmeter circuit,
$R_o=25+9975=10000$

Resistance of meter with ${10}^{\circ }C$ rise in temperature
$R_{mt}=R_m(1+\alpha t)$
$=25(1+0.004\times 10)$
= 26 $\Omega$

Resistance of multiplier with ${10}^{\circ }C$ rise in temperature

$R_{st}=R_s(1+\alpha t)$

$=9975(1+0.00015\times 10)$

= 9989.96 $\Omega$

Total resistance of voltmeter circuit with ${10}^{\circ }C$ rise in temperature

$R_{at}=26+9989.96=10015.96\Omega$

Reading of voltmeter at ${10}^{\circ }C$ rise in temperature

$=\frac{10000}{10015.96}\times 10=9.984V$

Percentage error
$=\frac{9.984-10}{10}\times 100=0.16percentlow$