Each resistor in the three circuits in the drawing has the same resistance [tex]R[/tex], and the batteries have the same voltage [tex]V[/tex]. The values for [tex]R[/tex] and [tex]V[/tex] are [tex]6 \, \Omega[/tex] and [tex]6.0 \, \text{V}[/tex], respectively. Determine the total power delivered by the battery in each of the three circuits.

Question

23-12-2024
Physics

College

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Each resistor in the three circuits in the drawing has the same resistance [tex]R[/tex], and the batteries have the same voltage [tex]V[/tex]. The values for [tex]R[/tex] and [tex]V[/tex] are [tex]6 \, \Omega[/tex] and [tex]6.0 \, \text{V}[/tex], respectively. Determine the total power delivered by the battery in each of the three circuits.

Answer :

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Final Answer:

The total power delivered by the battery in each of the three circuits is 12.0 watts.

Explanation:

In all three circuits depicted, each resistor has the same resistance 'R' and is connected to a battery with the same voltage 'V'. The total power delivered by the battery in a circuit can be determined using the formula P = V² / R, where P is power, V is voltage, and R is resistance. Since the values for resistance (R) and voltage (V) are given as 6Ω and 6.0V, respectively, for all three circuits, the total power delivered by the battery can be calculated as P = (6.0V)² / 6Ω = 36.0V² / 6Ω = 6.0V² = 12.0 watts.

This calculation is applicable to each circuit because the power delivered by a battery in a simple circuit is determined solely by the voltage across the circuit and the resistance of the components. In these circuits, where all resistors have the same resistance and are connected to batteries with identical voltages, the total power delivered by the battery remains constant at 12.0 watts. Understanding this relationship between voltage, resistance, and power enables the determination of the total power delivered by the battery in each circuit without altering the calculations for each scenario.