Power In Electric Circuits

Battery Calculation: Equivalent Emf, Internal Resistance, and Current

(i): Calculating the Equivalent Emf

The two batteries are connected in parallel, so the equivalent emf $E_%7B%5Ctext%7Beq%7D%7D$ is calculated using the formula:

$E_%7B%5Ctext%7Beq%7D%7D%20%3D%20%5Cfrac%7BE_1%20r_2%20%2B%20E_2%20r_1%7D%7Br_1%20%2B%20r_2%7D$

Given values: $E_1%20%3D%203%20%5C%2C%20%5Ctext%7BV%7D%2C%20E_2%20%3D%206%20%5C%2C%20%5Ctext%7BV%7D%2C%20r_1%20%3D%200.2%20%5C%2C%20%5COmega%2C%20r_2%20%3D%200.4%20%5C%2C%20%5COmega$

Substitute the values into the equation:

$E_%7B%5Ctext%7Beq%7D%7D%20%3D%20%5Cfrac%7B(3%20%5Ctimes%200.4)%20%2B%20(6%20%5Ctimes%200.2)%7D%7B0.2%20%2B%200.4%7D%20%3D%20%5Cfrac%7B1.2%20%2B%201.2%7D%7B0.6%7D%20%3D%20%5Cfrac%7B2.4%7D%7B0.6%7D%20%3D%204%20%5C%2C%20%5Ctext%7BV%7D$

Thus, the equivalent emf of the combination is $4%20%5C%2C%20%5Ctext%7BV%7D$ .

(ii): Calculating the Equivalent Internal Resistance

The equivalent internal resistance $r_%7B%5Ctext%7Beq%7D%7D$ is given by:

$r_%7B%5Ctext%7Beq%7D%7D%20%3D%20%5Cfrac%7Br_1%20r_2%7D%7Br_1%20%2B%20r_2%7D$

Substitute the values:

$r_%7B%5Ctext%7Beq%7D%7D%20%3D%20%5Cfrac%7B(0.2%20%5Ctimes%200.4)%7D%7B0.2%20%2B%200.4%7D%20%3D%20%5Cfrac%7B0.08%7D%7B0.6%7D%20%3D%200.1333%20%5C%2C%20%5COmega$

Thus, the equivalent internal resistance of the combination is $0.1333%20%5C%2C%20%5COmega$ .

(iii): Calculating the Total Current

The total resistance in the circuit is the sum of the internal resistance $r_%7B%5Ctext%7Beq%7D%7D$ and the external resistor $R%20%3D%204%20%5C%2C%20%5COmega$ . Thus, the total resistance $R_%7B%5Ctext%7Btotal%7D%7D$ is:

$R_%7B%5Ctext%7Btotal%7D%7D%20%3D%20r_%7B%5Ctext%7Beq%7D%7D%20%2B%20R%20%3D%200.1333%20%2B%204%20%3D%204.1333%20%5C%2C%20%5COmega$

Using Ohm's law, the current $I$ drawn from the combination is:

$I%20%3D%20%5Cfrac%7BE_%7B%5Ctext%7Beq%7D%7D%7D%7BR_%7B%5Ctext%7Btotal%7D%7D%7D%20%3D%20%5Cfrac%7B4%7D%7B4.1333%7D%20%3D%200.968%20%5C%2C%20%5Ctext%7BA%7D$

Thus, the current drawn from the combination is $0.968%20%5C%2C%20%5Ctext%7BA%7D$ .

About Power In Electric Circuits - CBSE-CLASS-XII

Power In Electric Circuits is a vital chapter for CBSE-CLASS-XII aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Power In Electric Circuits PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Power In Electric Circuits carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Battery Calculation: Equivalent Emf, Internal Resistance, and Current

(i): Calculating the Equivalent Emf

(ii): Calculating the Equivalent Internal Resistance

(iii): Calculating the Total Current

About Power In Electric Circuits - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Power In Electric Circuits PYQs?

How to best use this analysis?

Power In Electric Circuits

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Battery Calculation: Equivalent Emf, Internal Resistance, and Current

(i): Calculating the Equivalent Emf

(ii): Calculating the Equivalent Internal Resistance

(iii): Calculating the Total Current

About Power In Electric Circuits - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Power In Electric Circuits PYQs?

How to best use this analysis?

Chapter Questions
1 MCQs