Question

The n rows each containing cells in series are joined in parallel. The maximum current is taken from this combination across an external resistance of $3\Omega$. If the total number of cells used is $24$ and the internal resistance of each cell is $0.5\Omega$, then which option is correct?

• A. $m=8,n=3$
• B. $m=6,n=4$
• C. $m=12,n=2$
• D. $m=2,n=12$

Answer 1

The correct option is C

$m=12,n=2$

Step 1: Given data

$\text{External resistance}=3\Omega$

$\text{Internal resistance}=0.5\Omega$

$m\times n=24$ …(1)

Step 2: To find

We have to determine the values of $m,n$

Step 3: Calculating $m,n$

When equivalent resistance is equal to external resistance of $3\Omega$, the current is maximum.

For maximum current in circuit:

$\text{Total resistance, R}=\frac{0.5m}{n}$

$3=\frac{0.5m}{n}$

$m=6n$ …(2)

After solving the equations (1) and (2) to get the values,

$$\begin{gathered} 6n\times n=24 \\ 6n^2=24 \\ {n}^2=4 \\ n=2 \end{gathered}$$

By substituting the value of n in equation 2, we get

$$\begin{gathered} m=6\times 2 \\ =12 \end{gathered}$$

So,

$m=12$,$n=2$.

Therefore, option C is correct.