introduction to topics 5 and 6 in ib physics

7/22/2019 Introduction to Topics 5 and 6 in IB Physics

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5.1 Electric Potential Difference

Kari Eloranta

2014

Jyvskyln Lyseon lukio

International Baccalaureate

January 16, 2014

Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)

5.1 Electric Potential Difference January 16, 2014 1 / 16
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5.1 Electric Potential Difference

A battery is an electrical device that converts chemical energy intoelectric energy.

A battery has two metallic connectors calledterminals.

There is anelectric potential differencebetween the terminals.

Electric Potential DifferenceElectric potential difference is the electric potential energy difference perunit charge between two points in an electric field.

The unit of electric potential is [E]/[Q]= J C1 = 1V(joule/coulomb=volt), according to italian physicist Alessandro Volta(1745 1827).

For example, in a 9 V battery the potential difference across theunpluggedterminals is 9 V.

Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)

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5.1 Electric Potential Difference Vand Electric Current I

The terminals are called positive and negative based on their electrical

properties.

The positive (+) terminal is at higher electric potential with respect tothe negative () terminal.

When the terminals of a battery are connected to an electric circuit,an electric current starts flowing in the circuit and inside the battery.

The battery sustains an electric potential difference across theterminals. As a result, anelectric fieldis established in the wires, andother circuit elements, such as resistors.

The field exerts an electric force on the electrons and protons in ametallic wire. However, only free electrons can move in the wire.

Electric force tries to accelerate the electrons, and the interactionsbetween the electrons and the metallic lattice oppose to motion. As a

result, a steady electric current flows in the wire. Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)

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5.1 Electric Current I

Electric Current

Electric potential difference is the electric potential energy difference per

unit charge between two points in an electric field.

By definition, the direction of electric current is from the higherpotential to the lower (the direction of movement of a positive chargein an electric field).

Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)5.1 Electric Potential Difference January 16, 2014 4 / 16
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5.1 Voltmeter and ammeter in a DC-circuit

A

V

V

I

AV V

I

Figure : Two equivalent circuit diagrams for the study of (I,V) properties of a

lamp. Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)5.1 Electric Potential Difference January 16, 2014 5 / 16
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5.2 Electric Circuits: Electromotive Force (emf)

R

AV

Rint

I

Figure : The diagram represents the emf and internal resistance Rint of a

battery.

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5.2 Emf and Internal Resistance

The electric potential difference across the terminals of a battery in anopen circuit is called theelectromotive force of the battery (emf).

Electromotive Force E (emf)

Electromotive force of a battery is the total energy per unit charge madeavailable by the chemical reactions in the battery.

The unit of emf is []= [V]= [E][q]= 1V.

Since in reality emf it is not a force, but energy per unit charge, wecall it by its abbreviation emf.

All real batteries have some internal resistance which we denote byRint.

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5.2 Potential Difference VAcross the Terminals

When a battery is connected to an electric circuit, a constant electriccurrent flows through the circuit and the battery.

When an electric current flows in the circuit, the electric potentialdifference across the terminals of a battery drops by the amount ofRintI, because of the potential drop due to the internal resistance of

the battery.

Potential Difference VAcross the Terminals of Battery

When an electric current Iflows through a battery that has an emfandinternal resistance Rint, the potential difference Vacross the terminals of

the battery isV = RintI. (1)

When no current flows in the circuit, the potential difference V acrossthe terminals equals the emf, that is, V = .

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DC Circuit Electric Potential Graphs

Because an ideal wire does not have resistance, it does not consume

energy.As a result, the electric potential does not change along an ideal wire.

An ideal battery does not have internal resistance. As a result, it onlysupplies energy to the circuit, it does not consume energy at all.

A real wire dissipates energy.

Resistance of a Wire

The resistance of wire of length land cross-sectional area A is

R= lA (2)

where is the resistivity of the material the wire is made of.

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6.2 Electric Field Lines

A static electric charge creates an electric field around it.

Point charge is a small electrically charged object such as a proton orelectron, or any charged object for which the size of the object is smallcompared to its distance to other objects.

The electric field is illustrated by electric field lines.

The density ,of electric field lines illustrate the strength of the field.

By definition the direction of field lines is away from positive chargeand towards the negative.

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6.2 Electric Field Strength E

The electric field created by a positive point charge.

+

Figure : A positive point charge creates an outward radial electric field.

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9.3 Electric Field, Potential and Energy

Gravitational and electric fields are conservative fields, where work

done by the field on the object, as the object moves from point A toB, depends only on the location of the points, not on the path alongwhich the object moves from point A to B. That is, the work done inmoving a point charge between two points in an electric field isindependent of the path taken.

Consider a positive test charge Qtest, initially infinitely far away from apoint charge Q.The change in the electric potential energy Epot ofthe field is defined as the negative of the work done Wby the field onthe object, that is, W = Epot.

By using integral calculus, it is possible to show that the change inelectric potential energy is Epot = k

QQtestr

wherek= 8.99109 N m2 C2, and r is the distance to the point charge.

If we choose electric potential energy to be zero at infinity, we have an

equation for electric potential energy. Kari Eloranta 2014 (Jyvskyln Lyseon lukio International Baccalaureate)5.1 Electric Potential Difference January 16, 2014 12 / 16
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9.3 Electric Potential Energy

Electric Potential Energy Epot

If the electric potential energy infinitely far away from a point charge q iszero, the electric potential energy at distance r from the point charge q is

Epot = kqQtest

r(3)

where k= 8.99109 N m2 C2 is the electric constant in vacuum.

Electric potential energy is a property of theelectric field created bytheinteracting charges qandQtest.

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9.3 Electric Potential

Electric Potential

Electric potential is the work done per unit charge in bringing a positivetest charge Qtest to distance rfrom a point charge q.

Electric Potential V

If the electric potential infinitely far away from a point charge qis zero, theelectric potential at distance rfrom the point charge is

V =Epot

Qtest= k

q

r (4)

where k= 8.99109 N m2 C2 is the electric constant in vacuum.

Electric potential is a property of theelectric field created by the pointcharge q.

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9.3 Change in Electric Potential

Electric Potential Difference

Electric potential difference is electric potential energy difference per unitcharge between two points in an electric field.

Electric Potential Difference V

The electric potential difference in an electric field is

V =Epot

q(5)

where Epot is the change in electric potential energy, and q is the electriccharge of the object placed in the electric field.

The electric potential difference depends only on the properties of theelectric field.

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9.3 Electric Potential and Electric Field

Relation Between Electric Potential and Electric Field StrengthThe magnitude of electric field strength is

E=V

x (6)

where V is the change in electric potential, and x is the distance.

If the electric potential does not change between the points in

comparison, the electric field is zero.The greater the density of equipotential lines in the distance x, thegreater the electric field strength.

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introduction to topics 5 and 6 in ib physics

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