Question

Open circuit voltage of a source is 7.86 V and its short circuit current is 9.25 A. Find the current when an external resistance of 2.4Ω is connected
A. 1.4A
B. 1.82A
C. 2.01A
D. 2.4A

Answer 1

Battery is the source of emf and it drives the flow of current. Usually batteries will have some internal resistance and this helps from damage that might be caused when the circuit is short circuited. Current and potential difference across the battery will be affected when the battery is short circuited. We can determine them by using ohm’s law. We will solve this question using ohm’s law
Formula used:
${V_{eff}} = i{R_{eff}}$

Complete step by step solution:
Rate of flow of charge is known as current. A material which allows current to pass through it is known as a conductor. The property to hinder the flow of current is called resistance and a device which does that is known as a resistor.
In order to determine the amount of current that will flow when the battery is short circuited we should find out the total resistance that will be present in the circuit when the short circuit happens.
When a short circuit happens the only resistance that is present in the circuit will be internal resistance of a battery.
By using ohm's law we have
$\Rightarrow {V_{eff}} = i{R_{eff}}$
\eqalign{ & \Rightarrow i = \dfrac{E}{r} \cr & \Rightarrow 9.25 = \dfrac{{7.86}}{r} \cr & \therefore r = 0.85 \cr}
Where ‘E’ is the emf of a battery and ‘r’ is the internal resistance of a battery and ‘i’ is the current flowing. Hence when the battery is short circuited current will not become zero.
When external resistance of ‘R=2.4 Ohms’ is connected, then
\eqalign{ & {V_{eff}} = i{R_{eff}} \cr & \Rightarrow 7.86 = i\left( {2.4 + 0.85} \right) \cr & \Rightarrow i = \dfrac{{7.86}}{{3.249}} \cr & \therefore i = 2.4A \cr}

Hence, option D is correct.

Note:
Short circuited in the sense there will be only one effective resistance and that is internal resistance of the battery. If there is no internal resistance then theoretically infinite current will flow which causes damage to the battery. By using kirchhoff's voltage loop law we can determine the current flowing in the circuit if voltage and resistance is known.