Question

In the given circuit, find out the equivalent resistances across the points A and B when:
(i) \(V_A > V_B\), (ii) \(V_A < V_B\).
\includegraphics[width=0.5\linewidth]{imagej.png}

Hint:

In circuits with series resistors, simply add the resistances. For parallel resistors, use the reciprocal sum to find the equivalent resistance.

Answer 1

The given circuit consists of resistors of values \(200~\Omega\), \(50~\Omega\), and \(173~\Omega\), with a voltage difference between points \(A\) and \(B\). We need to find the equivalent resistance when: - (i) \(V_A > V_B\), - (ii) \(V_A < V_B\).
For this circuit, when \(V_A > V_B\), the resistors will be connected in series, and the equivalent resistance is the sum of the individual resistances. Thus, the equivalent resistance \(R_{\text{eq}}\) will be:
\[ R_{\text{eq}} = 200 + 50 + 173 = 423~\Omega \] For the second case, when \(V_A < V_B\), the resistors will be in parallel. The equivalent resistance for parallel resistors is given by the reciprocal sum of the individual resistances:
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{200} + \frac{1}{50} + \frac{1}{173} \] Solving this:
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{200} + \frac{1}{50} + \frac{1}{173} = 0.005 + 0.02 + 0.00578 = 0.03078 \] Thus, the equivalent resistance is:
\[ R_{\text{eq}} = \frac{1}{0.03078} \approx 32.5~\Omega \]