In a Wheatstone bridge, three known resistances are $R_{1} = 10 Ω$ , $R_{2} = 20 Ω$ , and $R_{3} = 30 Ω$ . The bridge is balanced when the galvanometer shows zero current. Find the value of the unknown resistance $R_{x}$ placed opposite $R_{3}$ .

hard 3 marks Class 12 · Physics · Current Electricity

Answer

R_{x} = 15 Ω

The correct answer is $R_{x} = 15 Ω$ — Calculate: $R_{x} = 15 Ω$ .

Step-by-step solution

For a balanced Wheatstone bridge, the ratio of the two resistances in one branch equals the ratio in the other branch: $\frac{R _{1}}{R _{2}} = \frac{R _{x}}{R _{3}}$ .
Substitute the known values: $\frac{10}{20} = \frac{R _{x}}{30}$ .
Simplify the left side: $\frac{10}{20} = 0.5$ .
Cross‑multiply: $0.5 \times 30 = R_{x}$ .
Calculate: $R_{x} = 15 Ω$ .

Common mistake: Using the wrong ratio (e.g.,

R_{1} / R_{3} = R_{x} / R_{2}

) which leads to an incorrect value.

Concept tested: Balanced Wheatstone bridge condition