Question

Three resistors of 2Ωeach are connected in parallel with a 3V battery. Calculate the effective resistance and hence the effective current in the circuit.

Answer 1

Answer:

Hence, the effective and equivalent resistance of the circuit = 0.67 Ω

Hence, the current through the circuit = 0.045 A

Explanation:

Given,

Number of resistors = 3

Resistance of each resistor = 2 Ω

So,

R1 = 2 Ω

R2 = 2 Ω

R3 = 2 Ω

Potential Difference of the Battery = 3V

Let the effective resistance of the circuit be 'R(eq)' where 'eq' demonstrates the equivalent resistance of the circuit.

Since the resistors are connected in parallel, then,

R(eq) = R(eq - P) (where P stands for parallel combination)

We know that

1 / R(eq - P) = 1 / R1 + 1 / R2 + 1 / R3

=> 1 / R(eq) = 1 / 2 + 1 / 2 + 1 /2

=> 1 / R(eq) = 3/2

=> R(eq) = 2/3 = 0.67 Ω

Hence, the effective and equivalent resistance of the circuit = 0.67 Ω

Now let the current through the circuit be 'I'.

Then by ohm's Law, we know that,

Resistance = Potential Difference / Current

=> R = V / I

Then wr can derive that ,

=> I = V / R

By applying values , we get,

=> I = 3 / 0.67 = 0.0447 A = 0.045 A

Hence, the current through the circuit = 0.045 A

'A piece of Supplementary Counsel' :-

• Resistance = Resistance is a measure of the opposition to current flow in an electrical circuit. All materials resist current flow to some degree

• Potential Difference = Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points.

• Current = An electric current is the rate of flow of electric charge past a point or region. An electric current is said to exist when there is a net flow of electric charge through a region. Electric charge is carried by charged particles, so an electric current is a flow of charged particles.