In the part of a circuit shown in figure, determine the current through 20 $\Omega$ resistance, if Potential at 'A' is 30 V, Potential at B = Potential at C = 20 V:
figure [H]
figure
Show Hint
Current always flows from higher to lower potential.
Step 1: Understand the layout from the numbers. Point $A$ is at $30\,\text{V}$, while points $B$ and $C$ are both at $20\,\text{V}$. The $20\,\Omega$ resistor is one branch carrying current from $A$ toward $B$ (or $C$). Step 2: The rule for a single resistor branch. The current through any resistor is set by Ohm's law using the potential difference across its own ends: \[ I = \frac{V_{\text{across}}}{R}. \] Step 3: Find the potential difference across the $20\,\Omega$ resistor. One end is at $A = 30\,\text{V}$ and the other end is at $20\,\text{V}$, so \[ V = 30 - 20 = 10\ \text{V}. \] Step 4: Apply Ohm's law. \[ I = \frac{10}{20} = 0.5\ \text{A}. \] Step 5: Why $B$ and $C$ being equal matters. Since $B$ and $C$ sit at the same potential, the drop across the $20\,\Omega$ branch is cleanly $10\,\text{V}$, and the result does not depend on the other branches. Step 6: Conclusion. The current through the $20\,\Omega$ resistor is $0.5\,\text{A}$. \[ \boxed{0.5\ \text{A}} \]
