Question

Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.

Short answer

The internal resistance of the cell is \(0.2\Omega \) and the minimum voltage output needed to charge the battery is \(10\;V\)

Step-by-step solution

Definition of RC constant and resistance

RC time constant: This measurement informs us how long it will take a cap to charge to a particular voltage level.

Anything that prevents current flow is referred to as "resistance" in this context.

Given information

\(\begin{align}{}V = 10\;V\\emf = 12\;\\VI = 10\;A\end{align}\)

Formula Used:

The\(RC\)constant is calculated as

\(\tau = R \times C\)

Where \(R\) is resistance and \(C\) is capacitance.

Constructing circuit

Consider a camcorder with resistance \(R\) is attached to a lithium cell as shown below:

Use the below information to find the required information.

\(\begin{align}{}V = 5\;V\\R = 10k\Omega \\T = 5\;msn\end{align}\)

Calculating Voltage

Now, calculate the voltage through the terminal of the battery.

\(\begin{align}{}V & = emf - Ir10\;\\V & = 12\;V - (10\;A)r - 2\;\\V & = - (10\;A)r\end{align}\)

\(\begin{align}{}(10\;A)r & = 2\;V\\r & = \frac{{2\;V}}{{10\;A}}\\r& = 0.2\Omega \end{align}\)

Hence, the minimum voltage output of a battery charger will be terminal voltage.

Thus, the minimum voltage output is \(10\;V\).