Question

a)The current in the circuit shown in the figure is 0.20 A. What is the potential difference ΔV_bat across the battery traveling in the direction shownin the first figure?

b)Find the current I in the circuit shown in the second figure.

Answer 1

Concepts and reason

The concepts required to solve the problem is Ohm’s law and finding the equivalent resistance for the combination of resistors.

First, find the potential difference across the battery using Ohm’s law. Then, find the current in the circuit by finding the resulting resistance and then by using Ohm’s law.

Fundamentals

Ohm’s law is a relation connecting the current, voltage and resistance in an electric circuit. Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference across two points. The constant of proportionality is called the resistance of the circuit.

The expression for the ohm’s law is,

Here, is the potential difference, is the current, andis the resistance.

When two resistorsand are connected in series, the resultant resistance is,

(a)

According to Ohm’s law, the potential difference across the battery is,

Substitute forand forin the equation to find the potential across the battery.

(b)

In the figure, the resistors are connected in series. For a series combination of resistors, the equivalent resistance is,

Substitute for and for in the equation to find the equivalent resistance.

According to Ohm’s law, the current in the circuit is,

Substitute for and for to find

Ans: Part a

The potential difference across the battery is.

Part b

The current in the circuit is