## Note on Potential Difference, Electromotive Force and Ohm's Law

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#### Potential difference and electromotive force

A positively charged body is said to be at positive potential or higher potential. A negatively charged body is said to be at negative potential or lower potential.

Potential difference is defined as the amount of work done in moving a unit positive charge from one point to another in an electrical circuit. The unit of p.d (V) is JC-1 which is called volt.

Potential difference (V) = IR

#### Electromotive force (e.m.f.)

The e.m.f. of an electric source is the rate at which energy in a non-electrical form is converted into an electrical form during the passage of unit positive charge through it.

##### Voltmeter

Voltmeter is an electrical device which measures potential difference between any two points in an electric circuit.

Difference between emf and pd

 e.m.f p.d. It is a measure of the energy supplied by a source to carry a unit charge through a circuit. It is a measure of the work done while taking a unit charge from one point to other through a circuit. It is a cause of p.d. It is an effect of e.m.f. It is measured in an open circuit. It is measured in a closed circuit. It is greater than p.d. It is less than e.m.f.

#### Ohm’s law

The electric current passing through a conductor is directly proportional to the potential difference across its two ends at a constant physical condition. (Temperature, cross-sectional area, length, shape, nature of material etc.)

If ‘I’ is the electric current through a wire and ‘V’ is the p.d. across its ends.

I α V

V α I

V= IR………… (i) where R= electrical resistance of the conductor, which is used as constant.

From equation (i), we have

R = $$\frac{V}{R}$$

R is an electrical resistance of the conductor, which is considered as constant.

Here, I = Electric current

V = Potential difference

R = Resistance

According to the above relationship, resistance is the ratio of the potential difference across its two ends to the electric current flowing through it.

##### Experimental verification of Ohm's law

The experimental set up for the verification of the Ohm's law is shown in the figure. The given figure consists of a voltmeter (V) which is connected across a nichrome wire BC. The wire BC is connected with an ammeter (A), a key K and cells. The ammeter measure the current (I) through the circuit whereas the voltmeter measure the p.d. (V) across the wire PQ.
At first use a single cell. When the key K is closed, electric current flows in the circuit. Record the readings of the ammeter and the voltmeter. Repeat the experiment by using two cells and joining M and O. Now, join M and R and record the readings of ammeter and voltmeter. When we plott a graph between p.d (V) and current (I) and get a straight line through the origin as shown in the figure, this shows that the current indirectly proportional to the p.d. which verifies Ohm's law.

• The e.m.f. of an electric source is the rate at which energy in a non-electrical form is converted into an electrical form during the passage of unit positive charge through it.
• Voltmeter is an electrical device which measures potential difference between any two points in an electric circuit.
• According to the Ohm's law, 'The electric current passing through a conductor is directly proportional to the potential difference across its two ends at a constant physical condition.'
• Resistance is the ratio of the potential difference across its two ends to the electric current flowing through it.
.

### Very Short Questions

'60 W' written in an electric bulb, 60 Joules of electrical energy is converted into heat and light energy in one second.

Before the discovery of electron, it was believed that there is the flow of positive charge from a positively charged body to a negatively charged body. This concept is still in use which is called conventional current.
But in actual practice, the direction of electron flow is the actual flow of electric current which is opposite to the conventional current.

An electric circuit through which electricity flows is called a closed circuit. An electric circuit through which electricity does not flow is called a closed circuit.

1. Electric bulb
2. Cell
3. AC source
4. Switch
5. Voltmeter
6. Ammeter

When positive terminal of one point is connected to negative terminals of other point, it is called series combination. Similarly, when positive terminals are connected at a point and negative terminals are connected to another point, it is called parallel combination.

Ammeter is connected in series because it has low resistance and hence it measures current in the circuit without any appreciable potential drop across it.

But, voltmeter is connected in series because it has high resistance and hence it measures potential difference across the device without causing any appreciable decrease in current through a device.

Voltmeter is connected in parallel combination.

Potential difference is defined as the amount of work done in moving unit positive charge from one point to another in an electrical circuit. Its unit is Volt(V).

The potential difference (pd) between any two points in an electric circuit is said to be 1 V if 1 J of work is done in moving 1C charge between these two points.

Electromotive force (e.m.f) is the energy supplied by the cell per unit charge passing through the circuit. Unit of emf is volt but it is also described as the energy in joules available from the cell per coulomb of charge.

 e.m.f Pd It is the energy supplied by the cell per unit charge passing through the circuit. It is the work done in moving a unit positive charge from one point to another. It is greater than p.d. It is less than e.m.f.

The property of any material to resist the flow of charges through it is called resistance. Its SI unit is ohm (Ω).

• Length of the conductor
• Cross-sectional area of the conductor
• Material of which the conductor is made
• Temperature of the conductor
• Shape of the conductor

We know that resistance of the conductor is

• directly proportional to the length i.e. R ∝ ρ
• inversely proportional to its cross sectional area
R ∝
Combining those two relations,
R ∝
or, R = ρ
∴ ρ = .

Ohm's law state that the current flowing through a resistor is directly proportional to the potential difference applied across it, provided the temperature and other physical conditions are constant.
i.e. I ∝ V
or, V ∝ I
or, V = IR where 'R' is the proportionality constant called resistance.

If a current of 1 A through a conductor maintains a p.d. of 1V across its ends, then its resistance is called 1Ω.

The resistivity is the characteristics of the material of the wire. So, it does not change even if its length is tripled.

The conductors which obey the ohm's law are known as ohmic conductor whereas those conductors which does not obey ohm's law are known as non-ohmic conductor. Example of ohmic conductor is copper and non-ohmic is semiconductor (silicon, germanium).

A number of resistors are said to be in series combination if they are joined end to end in such a way that the same current passes through each of them.

Let us consider four resistors of R1, R2, R3 and R4 are connected in series combination such that V1, V2, V3 and V4 are the pds across R1, R2, R3 and R4 respectively. The net potential difference is
V = V1 + V2 + V3 + V4

Suppose 'I' be the current in the circuit, then pd across each resistors is
V1= IR1
V2= IR2
V3= IR3
V4= IR4
So, V = IR1 + IR2 + IR3 + IR4
or, = R1 + R2 + R3 + R4
∴ R = R1 + R2 + R3 + R4
Hence, the equivalent resistor in the series is the sum of all the individual resistor in the circuit.
R = R1 + R2 + R3

If the number of resistors are connected across the same potential, then it is said to be in parallel combination.

Let us consider four resistance, R1, R2, R3 and R4 connected in parallel such that current through each is I1 , I2, I3, I4
Here, total current will be I = I1 + I2 + I3+ I4 If V be the potential across each resistor I1 = , I2 = , I3 = , I4 = and
Now,
I = V (+ + +)
or, = V (+ + +)
or, = + + +
Hence, the equivalent resistance in parallel combination
= + + + ....................+

The name of instruments X and Y are ammeter and voltmeter respectively. Here, in figure, R is resistance and K is key. The direction of current flow is:

Current (I) = 1A
Time (t) = 30 min = 30 x 60 sec = 1800 sec
Charge (Q) = ?
Now,
By using formula,
I =
or, Q = I x t
= 1800 x 1
= 1800 C
Hence, 1800 C charge flows through the circuit.

Here,
Length (= 5m
Resistance (R) = 2Ω
Area (A) = 0.1 m2
Resistivity (ρ) = ?
Conductivity (σ) = ?
Now,
ρ = = = 0.04Ωm

And conductivity( σ) = = 1/0.04 = 25m/ohm

Resistance (R) = 20Ω
Current (I) = 0.25A
Pd of battery (V) = ?
Using ohm's law,
V = IR
or, V = 0.25 x 20
or, V = 5 V
Hence, the pd required to the battery is 5V.

Potential difference (V) = 30V
Current (I) = 5A
Resistance (R) = ?

By ohm's law,
V = IR
or, R = = = 6Ω
Hence, 6Ω resistance is occurred between these two points.

Given,
First resistance (R1) = 50Ω
Another resistance (R2) = 10Ω
Equivalent resistance (R) = ?
Current (I) = ?
Pd supply (V) = 12 V

As we know that, in series connection
R = R1 + R2
= 50 + 10
= 60Ω
Now, using Ohm's law,
V = IR
or, I =
or, I =
or, I = 0.2 A
Hence, equivalent resistance is 60Ω and current is 0.2A.

Given,
Power of heater (P) = 1000 W
Pd applied (V) = 220V
Current (I) = ?
By using formula,
P = I x V
or, 1000 = I x 220
or, I =
= 4.54 A
Hence, 4.54 A current flows through a heater.

Given,
Power of bulb (P) = 100 W
Pd supplied (V) = 220 V
Resistance of bulb (R) = ?

We know that,
P = I x V
or, I = = 0.45 A

Similarly, by using ohm's law,
V = IR
or, 220 = 0.45 x R
or, R = 220/0.45
or, R = 488.89 Ω
Hence, the resistance nearly 889Ω.

Here,
Here, X is voltmeter and Y is ammeter.
Y is connected in that way because it has low resistance and has no applicable loss of current.
Pd (V) = 20V
Resistance (R) = 3Ω
So, current that is measured by Y (I) = ?

Using V = IR,
I = = = 6.67A
Hence, Y instrument measures 6.67 A.

Here
Charge (Q) = 200C
Time (t) = 25s
Current (I) = ?

We have,
I = $$\frac{Q}{t}$$
= $$\frac{200}{25}$$
= 8A.

Therefore, the current through the conductor is 8A.

(i). In the given, the instruments P is voltmeter. The instruments Q is ammeter.
(ii). V = 2.4
R =0.8Ω
Current (I) = ?
By Ohm,s law,
V = IR.
$$\therefore$$ 2.4 = I (0.8)

OR,
I = $$\frac{2.4}{0.8}$$
= 3A

Therefore, the current through the circuit is 3A.

0%

Iron
Copper
Steel
Pure Water

Thermostat
Ammeter
Voltmeter
Fuse
• ### Atoms are electrically neutral because

They have no charge
The nucleus is neutral
Electrons and protons are equal in number
Adjacent atoms balance each other's charge

Ohm
Watt
Coulomb
Volt

Watt
Ampere
Volt
Ohm
• ### 1A current means that

6.25 X 10-18 electrons pass in 1 sec across the cross-section of the conductor of a open circuit
6.25 X 1018 electrons pass in 1 sec across the cross-section of the conductor of a open circuit
6.25 X 10-18 electrons pass in 1 sec across the cross-section of the voltmeter
6.25 X 1018 electrons pass in 1 sec across the cross-section of the conductor of a close circuit
• ### What does a galvanometer do?

Detect and measure very small flow of charge
Measure potential difference
Measure high magnitude of current
measure resistance
• ### What does a Ammeter do?

measure resistance
Measure potential difference
Measure high magnitude of current
Detect flow of charge in circuit
• ### What does a Voltmeter do?

Measure potential difference
Detect flow of charge in circuit
Measure high magnitude of current
measure resistance
• ### Why is Ammeter connected in a series but Voltmeter connected in parallel?

Because Ammeter can effect potential difference and Voltmeter can effect current
Because Ammeter has low resistance and Voltmeter has high resistance
Because Ammeter requires less electricity while voltmeter requires high electricity
Because Ammeter has high resistance and Voltmeter has low resistance
• ### How many electrons are flowing per sec through a conductor of resistance 5 ? and potential difference of 50 volt?

0.625 X 1018 electrons
6.25 X 1018 electrons
625 X 1018 electrons
6.25 X 1019 electrons

Ohm
Watt
Ampere
Volt
• ### Which is not a factor on which resistance depends?

Volume of conductor
Material of a conductor
Area of cross-section of the conductor
Length of conductor

Resistance
Velocity
Conductance
Friction

5X
9X
1.5X
6X

6X
1.5X
5X
9X
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