Question

For the circuit shown in the figure find the current through each resistor.

For the circuit shown in the figure find the potential difference across each resistor.

Answer 1

Concepts and reason

The concept required to solve the problem are equivalent resistance and ohm’s law.

The circuit diagram is given. Therefore, equivalent resistance of the circuit can be derived using combination of resistors. Further, as the voltage of the source is known, current through the circuit can be derived. Further, potential drop can across each resistor can be calculated using Ohm’s Law.

Fundamentals

Resistor is an electronic device that restricts passing of current through it. Resistors of different values can be connected in any combination in a circuit.

The equivalent resistance of the circuit is the total resistance to current in the circuit. The equivalent resistance for different combination can be divided into series combination of resistors and parallel combination of resistors.

Series combination:

In series combination, resistors are connected on the same branch. The current passing through series resistors is same.

Equivalent resistance for series combination is given by

Parallel combination:

In parallel combination, resistors are connected on different branch such that potential drop across them is same.

Equivalent resistance for parallel combination is given by

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

(a)

As resistorare parallel,

As are connected in series

As are parallel

As and 2are connected in series

Now, current through circuit

Substitute 24 V for and for

As

Current through both of them is same and equal to current through circuit

In , 8and $Re=8 $are connected parallel and have same resistance, current in them will be equally divided.

Therefore,

In , are in series, therefore, current though them is same and equal to 2A

In , are connected parallel, will be divided amongst them according to their resistance. Since is half the value of 12, the current passing through it will be double.

Therefore,

(b)

The voltage drops across each resistor can be given by

$V=IR $

Across resistor

Across resistor

Across resistor

Across resistor

As Across resistor

Ans: Part a

The current through each resistor is given by

Part b

The voltage-drop across each resistor is given by