Question

In a meter bridge the length of the wire is 100cm.the point at which will the balance be obtained if the two resistance are in the ratio 2:3 is
$\begin{align}
  & A.\text{ }20cm \\
 & B.\text{ }40cm \\
 & C.\text{ }28.6cm \\
 & D.\text{ }44.1cm \\
\end{align}$

Answer 1

Hint: Meter Bridge is generally used to calculate unknown resistance and length of wire where circuit will be balanced by using null point concept. So to use the balancing condition of the Meter Bridge here we need to calculate the balance point for that we have provided with a ratio of two resistances. This way calculates value by putting value in balancing condition.

Complete answer:

Question states that in a meter bridge the length of wire is 100cm i.e. AB = 100cm. Now we need to calculate the point where balance will be obtained. According to balancing condition of Meter Bridge,
$\dfrac{{{R}_{1}}}{{{R}_{2}}}=\dfrac{x}{100-x}.......(1)$
We have given the ratio of two resistances which is 2:3
$\dfrac{{{R}_{1}}}{{{R}_{2}}}=\dfrac{2}{3}$
Therefore, equation (10 implies
$\dfrac{2}{3}=\dfrac{x}{100-x}$
$\begin{align}
  & \Rightarrow 200-2x=3x \\
 & \Rightarrow 200=5x \\
 & \Rightarrow x=40cm \\
\end{align}$

Hence at the distance of 40cm is the point at which will the balance be obtained therefore correct option is (b).

Additional information:
In meter bridge if the wire is not uniform then its resistance will not be proportional to its length which is 1 meter so there may be an error while calculating unknown resistance of circuit In this kind of network concept of null point is used to get balance condition null point is also known as balance point.

Note:
Meter Bridge is the modification of Wheatstone’s network. Wheatstone’s network is used to determine the value of unknown resistance since, length of wire used is one meter i.e. 100cm therefore it is called a meter bridge. The balance condition for Wheatstone’s network can also be determined by using ohm’s law.