Question

The Wheatstone bridge shown in fig. here gets balanced when the carbon resistor used as ${R_1}$ has the colour code (orange, Red, Brown). The resistors ${R_2}$ and ${R_4}$ are 80 and 40 respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for carbon resistor, used as ${R_3}$, would be:

A) Red, Green, Brown.
B) Brown, Blue, Brown.
C) Grey, Black, Brown.
D) Brown, Blue, Black.

Answer 1

Resistor is an electrical component which has two terminals and it is used to decrease the flow of the current in the circuit. Wheatstone bridge is an arrangement of the resistors, ammeter, voltmeter, etc. and it is used to find the value of the unknown resistor.

Formula used:
The formula of the resistors in the balanced condition of the galvanometer is given by,
$\dfrac{{{R_1}}}{{{R_3}}} = \dfrac{{{R_2}}}{{{R_4}}}$
Where ${R_1}$ and ${R_3}$ are the resistors on one side of the galvanometer whereas ${R_2}$ and ${R_4}$ are resistors on the other side of the galvanometer.

Complete step by step solution:
It is given in the problem that Wheatstone gets balanced when the carbon resistor used as ${R_1}$ has the colour code (orange, Red, Brown) the resistors ${R_2}$ and ${R_4}$ are 80 and 40 respectively assuming that the colour code for the carbon resistors gives their accurate values then we need to find the colour code for resistor ${R_3}$.
When the current in the Galvanometer is balanced then the ratio of resistor are balanced on the either side of the galvanometer,
$\Rightarrow \dfrac{{{R_1}}}{{{R_3}}} = \dfrac{{{R_2}}}{{{R_4}}}$………eq. (1)
The colour code of the resistor ${R_1}$ is orange, red, brown which means the resistance would be 3,2,10 so the combined resistance would be$320\Omega$.
Replacing the value of resistance${R_1}$,${R_2}$, and ${R_4}$ in the equation (1)
$\Rightarrow \dfrac{{{R_1}}}{{{R_3}}} = \dfrac{{{R_2}}}{{{R_4}}}$
$\Rightarrow \dfrac{{320}}{{{R_3}}} = \dfrac{{80}}{{40}}$
$\Rightarrow \dfrac{{320}}{{{R_3}}} = 2$
$\Rightarrow {R_3} = 160\Omega$.
The resistance of the resistor ${R_3}$ is equal to ${R_3} = 160\Omega$. The colour code according to the resistance is equal to Brown, Blue and Brown.

The correct answer for this problem is option B.

Note: The Wheatstone is a very important topic and it is asked frequently to find the unknown resistance. When the current in the galvanometer is balanced then the ratio of the resistors are equal. The resistors are colour coded according to their resistance value.