Three resistors of 4 Ω, 6 Ω and 9 Ω are connected in parallel. Which resistor consumes the maximum power?

Explanation:

Power Consumption in Parallel Resistors:

Definition: When resistors are connected in parallel, the voltage across each resistor is the same, and the power consumed by each resistor is determined by the formula:

Power (P) = V² / R

Here:

• P: Power consumed by the resistor
• V: Voltage across the resistor
• R: Resistance of the resistor

Calculation:

Given three resistors with resistances 4 Ω, 6 Ω, and 9 Ω connected in parallel, the voltage across all resistors is the same due to the parallel configuration. The power consumed by each resistor is inversely proportional to its resistance. Therefore, the resistor with the smallest resistance will consume the maximum power.

Let us calculate the power consumed by each resistor:

• Power consumed by the 4 Ω resistor: P₄ = V² / 4
• Power consumed by the 6 Ω resistor: P₆ = V² / 6
• Power consumed by the 9 Ω resistor: P₉ = V² / 9

It is evident from the formulas that:

• The smaller the resistance, the larger the denominator in the formula for power consumption.
• Since the denominator is inversely proportional to the power consumed, the resistor with the smallest resistance (4 Ω) will consume the maximum power.

Conclusion:

Among the three resistors (4 Ω, 6 Ω, and 9 Ω), the 4 Ω resistor consumes the maximum power because power is inversely proportional to the resistance in a parallel configuration.

Correct Option: Option 1

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 6 Ω

The power consumed by the 6 Ω resistor is less than that consumed by the 4 Ω resistor because the resistance is higher. Using the formula P = V² / R, it is clear that increasing the resistance decreases the power consumption.

Option 3: 9 Ω

The power consumed by the 9 Ω resistor is the lowest among the three resistors because it has the highest resistance. In a parallel circuit, the resistor with the highest resistance consumes the least power.

Option 4: 17 Ω

This option is irrelevant to the given problem as there is no 17 Ω resistor mentioned in the circuit configuration. It does not apply to the scenario described.

Conclusion:

The correct answer is Option 1 (4 Ω) because the resistor with the smallest resistance in a parallel circuit consumes the maximum power. Understanding the relationship between power and resistance is crucial for analyzing circuits, especially when resistors are arranged in parallel. This principle is widely applied in electrical engineering and circuit design to optimize power distribution and efficiency.