Question

In order to measure the direct current in a wire, 5 A range ammeter is connected in series with it and indicates 4 amperes. When the 5 A range ammeter is replaced by 10 A range ammeter, the reading is 4.2 A. Both meter are known to be accurate and each produces full scale deflection for a 50 mV instrument drop. The value of current in the wire when neither meter is in the circuit is _______A.

• A. 4.42
• B. 44.2
• C. 0.442
• D. 4.2

Answer 1

The correct option is A 4.42

Resistance of 5 A range ammeter,

$R_1=\frac{50\times {10}^{-3}}{5}=0.01\Omega$

Resistance of 10 A range ammeter,

$R_2=\frac{50\times {10}^{-3}}{10}=0.005\Omega$

Let the resistance of wire, in which current to be measured is $r\Omega .$

Potential difference across wire and 5 A range ammeter
$=(r+0.01)4volts$

Potential difference across wire and 10 A range ammeter
$=(r+0.005)\times 4.2volts$

As potential drop is same in both cases

$(r+0.01)\times 4=(r+0.005)\times 4.2$

$or,r=\frac{0.019}{0.2}=0.095\Omega$

PD applied across wire
$=(0.095+0.01)\times 4$
$=0.42V$

$\therefore$ Current when neither meter is in the circuit is
$I=\frac{0.42}{0.095}=4.42A$