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:

For a Wheatstone bridge to be balanced, we apply the well-known balance condition

$$\dfrac{R_1}{R_2}=\dfrac{R_3}{R_4}.$$

We are told that the carbon resistor used as $$R_1$$ has the colour code (orange, red, brown). Before proceeding, let us translate this colour code into an actual resistance value.

The standard 3-band colour code for a carbon resistor is:

• First band → first significant digit
• Second band → second significant digit
• Third band → multiplier $$10^n$$

Using the colour-digit table (black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, grey = 8, white = 9), we have

$$R_1 :\; \text{orange (3)},\; \text{red (2)},\; \text{brown }(10^1).$$

So

$$R_1 = (3\,2)\times10^{1}\,\Omega = 32 \times 10 \,\Omega = 320\,\Omega.$$

The problem statement gives us

$$R_2 = 80\,\Omega,\qquad R_4 = 40\,\Omega.$$

Now we substitute these values into the balance condition:

$$\dfrac{R_1}{R_2} = \dfrac{R_3}{R_4}.$$

Rearranging to find the unknown $$R_3$$, we get

$$R_3 = R_1 \times \dfrac{R_4}{R_2}.$$

Substituting the numerical values,

$$R_3 = 320\,\Omega \times \dfrac{40\,\Omega}{80\,\Omega}.$$

Simplify the fraction inside:

$$\dfrac{40}{80} = \dfrac12 = 0.5.$$

Hence

$$R_3 = 320\,\Omega \times 0.5 = 160\,\Omega.$$

The next task is to convert $$160\,\Omega$$ into its colour code. Again using the 3-band scheme:

• First significant digit = 1 → brown
• Second significant digit = 6 → blue
• Multiplier required: $$10^{1}$$ (because $$16 \times 10^{1} = 160$$) → brown

Therefore, the colour sequence for $$R_3$$ is

brown, blue, brown.

Looking at the given options, this corresponds to Option B (which is numbered 2 in the list).

Hence, the correct answer is Option 2.