Question

A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be $100\Omega$. He finds the null point at ${l_1} = 2.9cm$. He is told to attempt to improve the accuracy. Which of the following is a useful way?
(A) He should measure ${l_1}$ more accurately
(B) He should change S to $1000\Omega$ and repeat the experiment
(C) He should change S to $3\Omega$ and repeat the experiment
(D) He should give up hope of a more accurate measurement with a meter bridge

Answer 1

A meter bridge is always balanced. In a meter bridge, the long wire measures 1m=100cm in length and it is made of constantan or manganin having a uniform area of the cross-section.
Formula Used: The formulae used in the solution are given here.
$\dfrac{{{l_1}}}{{100 - {l_1}}} = \dfrac{R}{S}$ where the symbols used imply the values given in the question.

Complete Step by Step Solution: A meter bridge also called a slide wire bridge is an instrument that works on the principle of a Wheatstone bridge. A meter bridge is used in finding the unknown resistance of a conductor as that of in a Wheatstone bridge.
It has been given that a resistance $R$ is to be measured using a meter bridge. Student chooses the standard resistance $S$ to be $100\Omega$. He finds the null point at ${l_1} = 2.9cm$.
As the meter bridge is balanced, it can be written that,
$\dfrac{{{l_1}}}{{100 - {l_1}}} = \dfrac{R}{S}$
Since ${l_1} = 2.9cm$ and $S = 100\Omega$, we assign the values in the above equation.
$\dfrac{{2.9}}{{100 - 2.9}} = \dfrac{R}{S} = \dfrac{R}{{100}}$.
$\dfrac{{2.9 \times 100}}{{100 - 2.9}} = R$
Simplifying the equation, we get that,
$R = \dfrac{{290}}{{97.1}} = 2.98\Omega \simeq 3\Omega$. The meter-bridge is of the same order. Therefore a student must use $3\Omega$ improve the accuracy of the measurement of resistance $R$.

Hence, the correct answer is Option C.

Note: A Wheatstone bridge is a kind of electrical circuit used in measuring an electrical resistance, which is unknown by balancing its two legs of the bridge circuit, where one of the legs includes an unknown component. Samuel Hunter Christie created this instrument in the year 1833 and was improved and also simplified by Sir Charles Wheatstone in the year 1843. The digital multimeters in today’s world provide the simplest forms in measuring the resistance. The Wheatstone Bridge can still be used in measuring light values of resistances around the range of milli-Ohms.