Question

A certain 6 V battery delivers 12 A when short circuited. How much current does battery deliver when $\mathbf{1}\mathbf{\Omega }$ resistor is connected to it?

Short answer

The current across resistor is $4\text{A}$.

Step-by-step solution

Identification of given data

The potential of battery is$V=6\text{V.}$

The short circuit current of battery is $I_{SC}=12\text{A}$.

The resistance of resistor is $R=1\Omega$.

Conceptual Explanation

The resistance for short circuit in battery is calculated then it is connected with given resistor in series to find the current across resistor.

Determination of current across resistor

The resistance for short circuit in battery is given as:

$R_{SC}=\frac{V}{I_{SC}}$

Substitute all the values in the above equation.

$$\begin{gathered} R_{SC}=\frac{6\text{V}}{12\text{A}} \\ {R}_{SC}=0.5\Omega \end{gathered}$$

The current across resistor is given as:

$I=\frac{V}{R+R_{SC}}$

Substitute all the values in the above equation.

$$\begin{gathered} I=\frac{6\text{V}}{1\Omega +0.5\Omega } \\ I=4\text{A} \end{gathered}$$

Therefore, the current across resistor is $4\text{A}$.