Topic: Network Theory
The resistance of a parallel circuit consisting of two resistors is 12 $\Omega$. One of the resistance wires breaks and the effective resistance becomes 18 $\Omega$. The resistance of the broken wire is
- A. 48 $\Omega$
- B. 18 $\Omega$
- C. 36 $\Omega$
- D. 24 $\Omega$
Answer: C. 36 $\Omega$
Explanation: For two resistors in parallel, $\frac{1}{R_{1}} + \frac{1}{R_{2}} = \frac{1}{12}$. If one breaks (say $R_{2}$ is left), the effective resistance is 18 $\Omega$, so $R_{2} = 18 \Omega$. Substituting this back gives $\frac{1}{R_{1}} = \frac{1}{12} - \frac{1}{18} = \frac{1}{36}$. Thus, $R_{1} = 36 \Omega$.