The correct option is 2 and 3 only
Explanation
In electrical circuits, resistors can be arranged in series or parallel. A parallel network consists of multiple resistors connected across the same two points (nodes). This configuration ensures that the electrical path splits, allowing current to flow through multiple branches simultaneously while maintaining a constant potential difference across the ends of each branch.
Statement-wise Analysis
- Statement 1 is Incorrect.
In a parallel circuit, all resistors are connected between the same two common points. Consequently, the potential difference (voltage) across each resistor is identical and equal to the source voltage, regardless of the resistance values of the individual branches. - Statement 2 is Correct.
According to the principle of conservation of charge (Kirchhoff’s Current Law), the total current entering a junction must equal the total current leaving it. In a parallel network, the main current divides into the various branches. Therefore, the total current is the algebraic sum of the individual currents flowing through each branch ($I = I_1 + I_2 + I_3 + \dots$). - Statement 3 is Correct.
The equivalent resistance ($R_{eq}$) of a parallel combination is calculated based on the fact that the total current is the sum of individual currents. Using Ohm’s Law ($I = V/R$), the relationship is derived as:
$\frac{V}{R_{eq}} = \frac{V}{R_1} + \frac{V}{R_2} + \dots$
Dividing by the constant voltage $V$, the formula becomes:
$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$
Thus, the reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances.
Key Takeaway
Parallel Circuits: Voltage remains constant across all branches, current splits inversely proportional to resistance, and the total resistance decreases, being always less than the smallest individual resistance in the network.