Question Video: Determining the Terminal Voltage of a Battery Physics • Third Year of Secondary School

Video Transcript

A battery has an internal resistance of 0.48 ohms. The electromotive force of the battery is 3.5 volts. What is the terminal voltage of the battery when it is connected to a circuit and there is a current of 650 milliamperes in the circuit? Give your answer to one decimal place.

In this question, we want to find the terminal voltage of a battery when it is connected to a circuit with a current of 650 milliamperes. Let’s begin by recalling the formula for the electromotive force, or emf, of a battery.

The emf 𝜀 of a battery is given by the equation 𝜀 equals 𝑉 plus 𝐼 times 𝑟, where 𝑉 is the terminal voltage of the battery, 𝐼 is the current in the circuit, and 𝑟 is the internal resistance of the battery. We can make the terminal voltage, 𝑉, the subject of the equation by subtracting 𝐼 times 𝑟 from both sides of this equation. This cancels the 𝐼 times 𝑟 on the right, leaving us with 𝜀 minus 𝐼 times 𝑟 equals 𝑉. We can then flip the equation so the 𝑉 is on the left, leaving us with 𝑉 equals 𝜀 minus 𝐼 times 𝑟.

Now that we have this equation in terms of 𝑉, let’s look at the other variables given to us in the question. The electromotive force of the battery is 3.5 volts, and the internal resistance of the battery is 0.48 ohms. We are also given 650 milliamperes as the current in the circuit. However, before using this value in the equation, we need to convert it into the SI units of current, amperes. 650 milliamperes is equal to 650 times 10 to the negative three amperes.

Now then, we can substitute these values into the equation. The terminal voltage of the battery 𝑉 is equal to 3.5 volts minus 650 times 10 to the negative three amps times 0.48 ohms. Completing the calculation, we find that the terminal voltage of the battery 𝑉 is equal to 3.188 volts. This answer, to one decimal place, is 3.2 volts. So, the terminal voltage of the battery when it is connected to this circuit is 3.2 volts.