# Finding the Potential Difference between the Two Points in Circuits with Examples

**Finding the Potential Difference between the Two Points in Circuits**

Potential difference between two points in circuit is the energy lost by the charge in being transferred from one point to another. For example, potential difference between A and B is found with following formula;

**V _{AB}=V_{B}-V_{A}=∑ε-∑i.R**

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This formula shows the energy lost by charge moving from point A to point B.

We should first find the direction of the current to determine values **∑ε **and** ∑i.R****. **If you take the sign of batteries having same direction with current as “+” then you must take oppositely connected batteries as “-“.

If the direction of the current and current passing through the resistor are the same then we take i.R as "+", if they are in opposite directions then we take i.R as "-".

In the circuit given below, if the direction of the current is shown like below, then potential difference between the points A-B and C-B are;

**V _{AB}=V_{B}-V_{A}= -ε_{2}-(+i.R_{1}+i.R_{2})**

**V _{CB}=V_{B}-V_{C}= -ε_{3}-(-i.R_{3})**

Example: Find the potential difference between the points A and B in the given circuit below.

Current of the circuit is in the direction of battery current.

Example: Find the power of the resistor R_{1}.

**ε _{eq}=ε_{2}-ε_{1}=34V-10V=24V**

Equivalent resistance of the circuit is;

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