# Finding Electric Potential at P, Q and R in a Earthed Circuit

• thereddevils
In summary, we are given a circuit with a point S that is earthed and we are asked to find the electrical potentials at points P, Q and R. Using Kirchoff's second law, we find that the current flows in the clockwise direction with a value of 2A. By applying Ohm's law and considering the direction of the current, we can calculate the voltage drops across each resistor. To find the potential at any point with respect to the reference point S, we simply add up the voltage drops across each piece. By doing so, we find that the potential at point Q is -9V and the potential at point R is -15V. Our reasoning is correct and we can also verify our answer by
thereddevils

## Homework Statement

In the circuit given (attached) , point S is earthed , what are the electrical potentials at point P , Q and R .

## Homework Equations

Kirchoff's second law .

## The Attempt at a Solution

The electric potential at point S is 0 . By applying Kirchoff's second law ,

I(2+3)=15-5

I=2A

i am not sure where to go from here .

#### Attachments

• electric potentials.bmp
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You found the current. In what direction does it flow? Use that to find the voltage drops across each resistor.

Doc Al said:
You found the current. In what direction does it flow? Use that to find the voltage drops across each resistor.

ok , the current is flowing in the clockwise direction . Could you elaborate a little further on the voltage calculation of each resistors ?

But the question is asking for the potential at points P,Q and R respectively . How is it related to the potential difference across the resistors .

Thanks !

thereddevils said:
ok , the current is flowing in the clockwise direction .
Good.
Could you elaborate a little further on the voltage calculation of each resistors ?
Sure. The voltage across each resistor is given by Ohm's law: ΔV = IR. To find the sign of the voltage across the resistor, you need to know the direction of the current. Hint: Does current across a resistor flow from lower to higher potential or from higher to lower?

But the question is asking for the potential at points P,Q and R respectively . How is it related to the potential difference across the resistors .
To find the potential at any point with respect to some reference, just add up the voltage drops across each piece. Here your reference is point S, which is marked as ground and thus is at 0 Volts. To find the potential of point P, for example, you need to find ΔV from S to P. S to P contains a battery, so what's ΔV? To find the potential of point Q, you'll add up the voltage drops across S-P and P-Q. What's the voltage drop from P to Q across that 2 Ω resistor?

Doc Al said:
Good.

Sure. The voltage across each resistor is given by Ohm's law: ΔV = IR. To find the sign of the voltage across the resistor, you need to know the direction of the current. Hint: Does current across a resistor flow from lower to higher potential or from higher to lower?

To find the potential at any point with respect to some reference, just add up the voltage drops across each piece. Here your reference is point S, which is marked as ground and thus is at 0 Volts. To find the potential of point P, for example, you need to find ΔV from S to P. S to P contains a battery, so what's ΔV? To find the potential of point Q, you'll add up the voltage drops across S-P and P-Q. What's the voltage drop from P to Q across that 2 Ω resistor?

thanks ! Now , i understand this question better . Let me attempt again .

Since the emf of the 15 V battery > emf of 5V battery , the current will be flowing in the clockwise direction .

pd across sp would simply be -5V .

pd across 2 ohm resistor is 2/(2+3) x (5-15)=-4V so pd across SQ is -5-4=-9V

pd across 3 ohm resistor is 3/(2+3) x (5-15)=-6V so pd across SR is -15 V

Are my reasonings correct ?

Perfecto!

Just for fun, realize that you can find the potential of a point (Q, say) by starting from S and going clockwise around the circuit or by going counter-clockwise. Do it both ways and check that you get the same answer.

Doc Al said:
Perfecto!

Just for fun, realize that you can find the potential of a point (Q, say) by starting from S and going clockwise around the circuit or by going counter-clockwise. Do it both ways and check that you get the same answer.

yay! Thanks ! Yeah , i have experimented with that

## 1. What is electric potential in a circuit?

Electric potential is a measure of the electric potential energy per unit charge at a specific point in an electric field. It is often referred to as voltage and is measured in volts (V).

## 2. How is electric potential calculated in a circuit?

The electric potential at a point in a circuit is calculated by dividing the electric potential energy by the charge at that point. In an earthed circuit, the electric potential is usually referenced to the earth or ground, which is considered to have a potential of 0V.

## 3. What is the purpose of finding electric potential in a circuit?

Finding the electric potential at specific points in a circuit can help determine the behavior of the circuit and the flow of electricity. It can also be used to calculate electric current and power in the circuit.

## 4. How is the electric potential at P, Q, and R in a earthed circuit determined?

The electric potential at P, Q, and R in an earthed circuit is determined by using Ohm's Law, which states that the electric potential is equal to the product of the resistance and current. It can also be calculated using Kirchhoff's Voltage Law, which states that the sum of the voltage drops in a closed loop must equal the sum of the voltage rises.

## 5. What factors affect the electric potential at P, Q, and R in a earthed circuit?

The electric potential at P, Q, and R in an earthed circuit can be affected by the voltage source, the resistance of the circuit, and the placement of the components in the circuit. Changes in any of these factors can cause a change in the electric potential at these points.

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