Question

The internal resistance of a 2.1 V cell which gives a current of 0.2 A through a resistance of 10 Ω is

• A. 1.0 Ω
• B. 0.2 Ω
• C. 0.5 Ω
• D. 0.8 Ω

Hint:

Ohm’s law will be used to calculate the internal resistance of the cell through the values.

Answer 1

The Correct Option is C

In the question, we have the values for external resistance, current, and voltage of the cell. As per ohm's law, these quantities are related to each other. Hence, ohm’s law will be used to calculate the internal resistance of the cell through the values.

Formula used:

As per ohm’s law, V = I(R+r)

• Where V is voltage, 
• I is current, 
• R is external resistance 
• r is internal resistance.

Complete step-by-step solution:

Given: Internal resistance = 2.1V, Current = 0.2A, external resistance = 10Ω.

To calculate internal resistance, we will use ohm’s law.

V = I(R+r)

2.1 = (0.2)(10+r)

\(⇒10+r=\frac{21}{2}\)

\(⇒r=\frac{21}{2}−10\)

r = 0.5 Ω

Thus, the internal resistance of the given cell is 0.5Ω.

Hence, the correct option is (C).

Note: The sum of internal and external resistance is the total resistance. 

Answer 2

\(I = \frac {E}{r + R } \Rightarrow 0.2 = \frac {2.1 }{ r + 10} \Rightarrow r = 0.5 \Omega\)

Answer 3

The current produced by a cell is equal to the voltage of the cell divided by the total resistance of the circuit. Using ohm's law formula and values, we can get the required answer.

Formula used:

The electric current produced by a cell is given as internal resistance and the voltage by the following expression.

\(I=\frac{E}{R+r}\)

Complete step-by-step answer:

We are given an electric cell whose voltage, amount of current and external resistance are given below respectively:

• E = 2.1 V
• I = 0.2 A
• R = 10Ω

Let r be the internal resistance of the cell. 

The current produced by a cell is given as internal resistance and the voltage by the following expression.

\(I=\frac{E}{R+r}\)

\(r=\frac{E}{I}−R\)

Putting all these values in the above expression for the internal resistance of the cell, we get

\(r=\frac{2.1}{0.2}−10=10.5−10=0.5Ω\)

Now, \(r=0.5Ω\) is the required value of internal resistance.

So, the correct answer is “Option C”.