Question

(a) Find the terminal voltage of a $\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{V}$motorcycle battery having a $\mathbf{0}\mathbf{.}\mathbf{600}\mathbf{\Omega }$internal resistance, if it is being charged by a current of $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{A}$(b) What is the output voltage of the battery charger?

Short answer

(a) The terminal voltage is$18V$.

(b) The output voltage of the battery is$18V$.

Step-by-step solution

Terminal voltage

The terminal voltage of the motor cycle battery is

$\mathbf{V}\mathbf{=}\mathbf{emf}\mathbf{-}\mathbf{lR}$

Here, emf is the output voltage of the battery,$\mathbf{l}$is the current and $\mathbf{R}$is the resistance

Calculation of terminal voltage

The motorcycle battery with an emf $\mathrm{E}=12\mathrm{V}$and internal resistance $r=0.6\Omega$. The battery is charged with a current of $\mathrm{l}=10\mathrm{A}$

(a) When a battery is charged, the charger generates a current that is the polar opposite of the current generated by the battery itself. The battery is charged as a result of this.

As a result, the battery's terminal voltage is

$$\begin{gathered} \mathrm{V}=\mathrm{E}+\mathrm{lr} \\ =12\mathrm{V}+\left(10\mathrm{A}\right).\left(0.6\mathrm{\Omega }\right) \\ =18\mathrm{V} \end{gathered}$$

Because the current is flowing in the other direction, the voltage drop across the internal resistance is of the opposite sign.

Calculation of output voltage

(b)As the charger is in parallel to the battery, its output voltage is the same as the battery's terminal voltage.

${\mathrm{V}}_{\mathrm{c}}=18\mathrm{V}$

The circuit diagram is shown below (the dashed rectangle is the entire battery, which includes the emf and the internal resistance).