What maximum power can be obtained from a battery of emf E and internal resistance r connected w

Name: Problem 1774, Chapter 12: JEE Physics
Uploaded: 2021-10-04T02:35:10-08:00
Duration: 1 min 19 s
Channel: Prem Bijarniya
Description: What maximum power can be obtained from a battery of emf E and internal resistance r connected with an external resistance R ? (A) (E^2 / 4 r) (B) (E^2 / 3 r) (C) (E^2 / 2 r) (D) (E^2 / r)

Step 1: We know that the power obtained from the battery is maximum when the external resistance

What maximum power can be obtained from a battery of emf E...

What maximum power can be obtained from a battery of $\mathrm{emf} \mathrm{E}$ and internal resistance $\mathrm{r}$ connected with an external resistance $\mathrm{R}$ ? (A) $\left(E^{2} / 4 r\right)$ (B) $\left(E^{2} / 3 r\right)$ (C) $\left(E^{2} / 2 r\right)$ (D) $\left(\mathrm{E}^{2} / \mathrm{r}\right)$

What maximum power can be obtained from a battery of $\mathrm{emf} \mathrm{E}$ and internal resistance $\mathrm{r}$ connected with an external resistance $\mathrm{R}$ ?
(A) $\left(E^{2} / 4 r\right)$
(B) $\left(E^{2} / 3 r\right)$
(C) $\left(E^{2} / 2 r\right)$
(D) $\left(\mathrm{E}^{2} / \mathrm{r}\right)$

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Key Concepts

Maximum Power Transfer Theorem

This theorem states that the maximum power is delivered to the load when the load resistance is equal to the internal resistance of the source. It is a fundamental principle in circuits which ensures that the energy transfer is optimized by matching the resistances of the source and the load.

Battery Internal Resistance and EMF

Every battery is characterized by an electromotive force (EMF) and an internal resistance. The internal resistance affects the current that the battery can deliver and plays a key role in determining the output voltage under load conditions, influencing the overall power transfer efficiency.

Electrical Power in Resistive Circuits

In resistive circuits, the power delivered to a component is calculated as the product of the square of the voltage across it and inversely proportional to its resistance. This concept is crucial to compute the power transferred to the load and to understand how variations in resistance impact energy consumption and efficiency.

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