Question

A battery of EMF \[10V\] and internal 3 ohm is connected to a resistor. If the current in the circuit is \[0.5A\], what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is:

Answer 1

Hint The EMF of the battery is given as \[10V\]and it is said that the battery has an internal resistance 3 ohms and is connected to a circuit with a resistor R. Now, the current flowing through the circuit is said as . \[0.5A\]. Calculate R value using ohm’s law and calculate V value at terminal using the obtained R value.

Complete Step By Step Solution
It is given that a closed circuit consists of a battery giving an EMF of \[10V\]to the circuit. There is a small internal resistance present inside the battery due to impedance in the supply. The value of this internal resistance is said to be 3 ohms. Now , ohm’s law states that the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor. Mathematically,
\[ \Rightarrow V = IR\]
The total resistance in the circuit is said to be the sum of resistance offered by the resistor R and the internal resistance of the battery component r. This implies that,
\[ \Rightarrow V = I(R + r)\]
Taking \[I\] to the other side , we get
\[ \Rightarrow \dfrac{E}{I} = (R + r)\]
Now, substitute the given values on the above equation.
\[ \Rightarrow \dfrac{{10}}{{0.5}} = (R + 3)\]
On simplifying , we get R value as
\[ \Rightarrow R = 20 - 3 = 17\Omega \]

Now, we need to find the terminal voltage across the circuit. For this, again we deploy ohms law and find the terminal voltage value.
\[ \Rightarrow V = IR\]
Now, we know the values of both I and R. Substituting , we get
\[ \Rightarrow V = (0.5) \times 17\]
\[ \Rightarrow V = 8.5V\]

The resistance of resistor R is \[17\Omega \] and the terminal voltage is \[8.5V\].

Note Terminal voltage is defined as the potential difference that is observed across the terminals of the source battery. It is said that if the battery is not connected with the circuit, then the observed terminal voltage is equal to that of EMF of the battery.