Question

Compared to an ideal battery, by what percentage does the battery's internal resistance reduce the potential difference across the 20 ohm resistor in the figure ?

Answer 1

Concepts and reason

The concept required to solve the given question is Ohm’s law.

First, find the net resistance of the circuit. Then, calculate the total current in the circuit by applying the Ohm’s law. After that, find the potential difference across the resistor. Finally, calculate the percentage loss in potential difference across this resistor.

Fundamentals

Ohm’s law gives the relation between current, voltage and resistance. The law states that the “electric current is directly proportional to the voltage and inversely proportional to the resistance of the circuit”.

Expression for Ohm’s law is given by,

Here, V is the voltage, I is the current and R is the resistance of the circuit.

The resistors combine in series or in parallel to form resistor combination. The equivalent resistance of two resistors that are combined in series is given by,

Here, is the equivalent resistance, , is the resistance of individual resistors.

Consider the given circuit; here the resistors, and are in series.

The equivalent resistance of the circuit is,

Substitute for , for and for . The equivalent resistance is,

Net current in the circuit,

Substitute for and for . The current is,

Potential difference across the resistor,

Here, is the potential difference across the resistor .

Substitute for and for . The potential difference is,

Resistance of the circuit without considering the internal resistance of the battery is,

Substitute for , and for . The resistance of the circuit without considering the internal resistance of the battery is,

The current in the circuit is,

Substitute for and for .

The potential difference of across the resistor is,

$V=R $

Substitute for and for . The potential difference is,

Hence the percentage loss in potential difference is,

Substitute for and for .

Ans:

The percentage potential difference across the resistor 2 is .