Question

When several resistors are connected in parallel in a circuit, what happens to the current and the equivalent resistance?

• A. Current divides among resistors, equivalent resistance decreases.
• B. Current remains the same, equivalent resistance increases.
• C. Current divides among resistors, equivalent resistance increases.
• D. Current remains the same, equivalent resistance remains the same.

Hint:

Adding a resistor in parallel always decreases the equivalent resistance of the circuit.
This is analogous to opening more lanes on a highway, which reduces the overall traffic resistance.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to identify the behavior of electric current and equivalent resistance when multiple resistors are connected in a parallel configuration across a voltage source.

Step 2: Key Formula or Approach:
For a parallel combination of resistors:
\[ I = I_1 + I_2 + \dots + I_n \]
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \]

Step 3: Detailed Explanation:

• In a parallel circuit, all resistors are connected across the same two nodes, meaning they experience the same potential difference (\(V\)).

• The total current (\(I\)) entering the parallel junction splits into multiple branches. The current through each individual resistor depends on its resistance according to Ohm's law (\(I_i = V / R_i\)). Thus, current divides among the resistors.

• The reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.

• This mathematical relationship guarantees that the equivalent resistance \(R_{eq}\) is always less than the smallest individual resistance in the combination.

• Adding more parallel branches provides more pathways for the charge to flow, which reduces the overall opposition to the current, causing the equivalent resistance to decrease.


Step 4: Final Answer:
Therefore, the current divides among the resistors, and the equivalent resistance decreases.