Question

17. The p.d's measured across three resistors connected in series are 5 V, 7 V and 10 V, and the supply
current is 2 A. Determine (a) the supply voltage, (b) the total circuit resistance and (c) the values of
the three resistors.​

Answer 1

Answer:

a) Hence, total potential difference through the circuit = 22 V

b) Hence, total resistance through the circuit = 11 Ω

c) Hence, the three resistors connected in series are : 2.5 Ω, 3.5 Ω and 5 Ω

Explanation:

Given,

Measures of potential difference across the resistors :

V1 = 5 V

V2 = 7 V

V3 = 10 V

Current through the circuit, I = 2 A

Also, these resistances are connected in series. Then we know that,

In a series resistor network the individual resistors add together to give an equivalent resistance, ( RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.

Also, potential difference (V) gets divided between the components while the current remains same.

a) Here, we need to find the total potential difference of the circuit. Then,

Let the total potential difference through the circuit be 'V'.

So,

V = V1 + V2 + V3

=> V = 5 V + 7 V + 10 V

=> V = 22 V

Hence, total potential difference through the circuit = 22 V

b) Here, we need to find the total resistance of the circuit.

It is given that the resistors are connected in series.

Here, Current = I = 2 A

Potential Difference = V = 22 V

Let the effective equivalent resistance be R.

Then,

By applying ohm's law, we get,

Resistance = Potential Difference / Current

=> R = V / I

=> R = 22 / 2 = 11 Ω

Hence, total resistance through the circuit = 11 Ω

c) Given,

Since, potential difference gets divided in each component of series combination and current remains same , then,

R1 = V1 / I = 5 / 2 = 2.5 Ω

R2 = V2 / I = 7 / 2 = 3.5 Ω

R3 = V3 / I = 10 / 2 = 5 Ω

Hence, the three resistors connected in series are : 2.5 Ω, 3.5 Ω and 5 Ω

'A piece of Supplementary Counsel' :-

• 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.

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