Understanding Parallel Connection of Resistors

When resistors are connected in parallel, they are connected across the same two points in a circuit. This type of connection has distinct characteristics regarding voltage, current, resistance, and power compared to a series connection.

Key Characteristics of Parallel Resistor Circuits

• Voltage: The voltage across each resistor in a parallel connection is the same as the voltage across the entire combination. If the circuit is connected to a voltage source, this voltage is equal to the source voltage.
• Current: The total current entering the parallel combination divides among the individual branches. The current through each resistor depends on its resistance and the voltage across it (Ohm's Law: \(I = V/R\)). The total current is the sum of the currents through all individual branches.
• Resistance: The total resistance of a parallel combination is less than the resistance of the smallest individual resistor. The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances: \(1/R_{total} = 1/R_1 + 1/R_2 + ... + 1/R_n\).
• Power: The total power dissipated by the parallel combination is the sum of the power dissipated by each individual resistor. Power dissipated by a resistor can be calculated using \(P = VI = I^2R = V^2/R\).

Analyzing the Given Options

Let's evaluate each option based on the characteristics of parallel connections:

• Option 1: Voltage in each branch is different. This statement is incorrect. In a parallel connection, the voltage across each branch (and hence across each resistor) is the same.
• Option 2: Current in each branch is same. This statement is incorrect. The current divides among the branches. The current is the same only if all resistors have the same resistance. Otherwise, the current depends on the individual resistance values (\(I = V/R\)).
• Option 3: Total power is equal to sum of individual branch power. This statement is correct. In any electrical circuit, whether series or parallel, the total power consumed or dissipated by the circuit is equal to the sum of the power consumed or dissipated by each individual component in the circuit. For parallel resistors, \(P_{total} = P_1 + P_2 + ... + P_n\).
• Option 4: Total power is equal to power in any branch. This statement is incorrect. The total power is the sum of the power in *all* branches, not just one specific branch (unless there is only one branch, which wouldn't be a parallel connection of multiple components).

Therefore, the true statement for the parallel connection of resistors is that the total power is equal to the sum of individual branch power.