Question 300 of 380

The Wheatstone bridge shown in the figure below, 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 $80\Omega$ and $40\Omega$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as ${R}_{3}$, would be

Abrown, blue, black.Bbrown, blue, brown.Cgrey, black, brown.Dred, green, brown.

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Answer: (B) brown, blue, brown.

Colour band $A$ and $B$ indicate the first two significant figures of resistance in 'ohm', while the $C$ band gives the decimal multiplier i.e., the number of zeros that follows the two significant figures $A$ and $B$.
The last band $D$ indicates the tolerance in percentage about the indicated value or in other word, it represents the percentage accuracy of the indicated value.

For ${R}_{1}$, the given colour of the rings of a carbon resistor are orange, red, brown then, the value of resistance is
${R}_{1}=32\times {10}^{1}$
Condition for balance in the Wheat stone's bridge is
$\dfrac{{R}_{1}}{{R}_{3}}=\dfrac{{R}_{2}}{{R}_{4}}$

So, $\dfrac{320}{{R}_{3}}=\dfrac{80}{40}$

$∴{R}_{3}=160\Omega$, so colour coding of resistor ${R}_{3}$ is
Brown$\rightarrow 1$
Blue$\rightarrow 6$
Brown$\rightarrow 1$
$16\times {10}^{1}\Rightarrow 160\Omega$