How to Calculate Voltageand its Definition

Key Concepts

1. Using voltmeter in a circuit

2. Calculating Voltage

Introduction

When a free positive charge is moved from high potential to low potential, work is done by the charge. This work is done because of the potential difference across the charges. In this section, we will be relating potential energy due to charges and the potential difference created between the positive charges and negative charges. We are also going to apply the formula and calculate the potential difference when work done on or by the charges is given along with the amount of charge. The device which is used to measure this potential difference will be used in a circuit.

Explanation:

Relation between Potential energy and potential difference 

Consider a unit charge “q”. This charge “q” has some potential energy stored in it, known as electrical potential energy. Let us say some energy is applied to move it from one point to another. In applying this energy, work is done either by the object or on the object.  

The work done to move a charge from one point to another is the potential difference.  

Potential difference, ΔV =
Potential Energy, E/Charge, q

Voltage 

Potential difference is also known as voltage. It is measured in volts (V), voltage is the work done in moving a unit test charge.  

Mathematically,  

Voltage , V= Work done, W / Charge, q

As can be seen from the formula, its SI unit is Joule/ coulomb abbreviated as J/C, given the name volt (V) after Alessandro Volta. 

The term voltage you must have seen in few of the batteries or at the back of a few electrical equipment. This voltage is the common name for potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between the two points. For example, in the case of a battery, a 6V battery means the potential difference between both ends of the battery is 6 V.  

Figure 1: A battery 

The device which is used to measure this potential difference is known as voltmeter. It is connected in parallel across the two points where the potential difference needs to be measured. The reading obtained is in volts (V). 

The symbol used to denote this voltage in an electric circuit is                 . 

Questions and answers: 

1. You have a 12.0-V motorcycle battery that can move 6000 C of charge and a 12.0-V car battery that can move 70,000 C of charge. How much energy does each deliver? (Assume that the numerical value of each charge is accurate to three significant figures.) 

Answer: 

For the motorcycle battery,  

  q = 6000 C  

  ΔV = 12.0 V = 12.0 J/C 

  W = ΔV.q 

       = 12 × 6000 

     = 72,000 J 

For the car battery,  

  q = 70,000 C  

ΔV = 12.0 V = 12.0 J/C 

W = ΔV.q  

     = 12 × 70,000 

     = 8,40,000 J 

Not all this energy is available for use, and a small amount of the energy is dissipated internally. 

2. Potential difference is measured in ……………….. by using a ……………..placed in …………. across a component. 

Answer:  

The potential difference is measured in volts by using a voltmeter placed in parallel across a component. 

3. When a 12.0-V car battery powers a single 40.0-W headlight, how many electrons pass through it each second? 

Answer:  

Since battery loses energy and a 40 W headlight uses 40 joules per second, so 

W = –40 J 

V = 12 V = 12 J/C 

q =

WVWV

    =

− 4012− 4012

    = – 3.33 C 

Number of electrons,

nene

nene

  =

− 3.33 C−1.6 × 10− 19 C/e− 3.33 C−1.6 × 10− 19 C/e

      = 2.08 ×10¹⁹electrons 

Summary

• Potential difference between two points is the work done to move a point charge from one point to another.

V = w /q

• Work is done by the cell to move electrons through the wire.

• SI unit of electric potential is volt (V)

1 volt = 1 Joule / 1coulomb

• The device used to measure the potential difference across a component is a voltmeter.