Potential Difference, Electromotive Force and Ohm's Law
Subject: Science
Overview
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. This note provides an information on potential difference, electromotive force and Ohm's law.Potential Difference, Electromotive Force and Ohm's Law
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.
Things to remember
- 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.
- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.
Videos for Potential Difference, Electromotive Force and Ohm's Law
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Questions and Answers
What is meant by '60 W' written in an electric bulb?
'60 W' written in an electric bulb, 60 Joules of electrical energy is converted into heat and light energy in one second.
What is conventional current?
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.
Define Ammeter
Define Voltmeter
Define Galvanometer
What is meant by closed and open circuit?
Identify the following symbols
- Electric bulb
- Cell
- AC source
- Switch
- Voltmeter
- Ammeter
What do you mean by series and parallel combination?
Why is ammeter connected in series but voltmeter in parallel?
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.
How is voltmeter connected in an electric circuit? Show with a diagram.
What do you mean by potential difference? Write its SI unit.
What is meant by 1 V?
Define the term electromotive force (emf) with SI Unit.
Write any two differences between emf and pd
| 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. |
What is resistance? Write its unit.
On what factors does the resistance of a conductor depend?
- 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
Prove that ρ = 
, where ρ = resistivity, R = resistance, A = cross-sectional area of a wire and l = length of the wire.
- directly proportional to the length i.e. R ∝ ρ
- inversely proportional to its cross sectional area
Combining those two relations,
R ∝
or, R = ρ
∴ ρ =
.
State and prove Ohm's law.
i.e. I ∝ V
or, V ∝ I
or, V = IR where 'R' is the proportionality constant called resistance.
What do you mean by 1Ω resistance?
A wire is stretched to triple its length. What happens to its resistivity?
What are ohmic and non-ohmic conductor. Give an example of each.
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).
What do you mean by series combination of resistance?
In series combination of resistors, show that the total (equivalent) resistance is the sum of individual resistors.
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
What do you mean by parallel combination of resistors?
Show that in parallel combination of resistors, reciprocal of equivalent resistance is the sum of reciprocal of all individual resistor. i.e. 
= 
+ 
+ 
+ ....................+
Here, total current will be I = I1 + I2 + I3+ I4
If V be the potential across each resistor I1 = 
, I2 = 
, I3 = 
, I4 = 
andNow,
I = V (
+ 
+ 
+
)or,
= V (
+ 
+ 
+
)or,
= 
+ 
+ 
+
Hence, the equivalent resistance in parallel combination
= 
+ 
+ 
+ ....................+
Study the given diagram and write the name of the instruments X and Y. What are R and K? Show the direction of flow of current in the circuit. 
If 1 Ampere current flows for 30 minutes through a circuit, calculate the amount of charge passed?
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.
Find the resistivity of a 5m long wire if the resistance of the wire is 2? and its area of cross section is 0.1m2. Also, find the conductivity of the wire.
Here,
Length (
= 5m
Resistance (R) = 2Ω
Area (A) = 0.1 m2
Resistivity (ρ) = ?
Conductivity (σ) = ?
Now,
ρ = 
= 
= 0.04Ωm
= 1/0.04 = 25m/ohmA simple electric circuit having 20Ω resistor is connected to a battery to obtain a current of 0.25 A, find the voltage required to the battery.
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 between two points of a wire carrying current 5 A is 40 volt. Calculate the resistance between these points.
Current (I) = 5A
Resistance (R) = ?
By ohm's law,
V = IR
or, R =
= 
= 6Ω Hence, 6Ω resistance is occurred between these two points.
A 50Ω resistor is connected to a 10Ω resistor in series. Find the equivalent resistance of these two. Also, find the current through the circuit if it is connected to 12V supply.
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.
What is the current flowing through a heater of 1000W when it is connected to 220 Volt?
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.
A bulb of 100 W is connected to 220V, what is the resistance of the filament bulb?
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.
Study the following figure and answer the given questions.
- Name the instruments X and Y.
- Why is Y connected in that way?
- Find the value that Y measures if pd is 20V.
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 =
= 
= 6.67AHence, Y instrument measures 6.67 A.
Calculate the current through a conductor when 200C charge flows through in it in 25 seconds.
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.
Study the following figure to answer the questions:
(i). Name the instruments P and Q.
(ii). In an experiment if p.d. across R is 2.4V and R= 0.8Ω , what will be the current through the circuit?
(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.
Quiz
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