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When the current flows through the electrolyte present in an electrolytic cell, the solution offers internal resistance to the flow of current across it. When the current doesn’t flow through the circuit, then the potential difference in such a condition is termed electromotive force.
Emf of a cell
An electric cell has potential due to the positive and negative electrodes immersed in an electrolyte solution. In the absence of current, the potential of electrolytes is the same throughout. This potential difference between the positive electrode (anode) and the negative electrode (cathode) in an open circuit is called the electromotive force (emf) of a cell, denoted by ε.
(V+) = Potential difference of positive terminal
(V-) = Potential difference of negative terminal
(V+) + ( V-) = Potential difference between P and N
V = Potential difference between P and A
+ Potential difference between A and B
+ Potential difference between B and N
= ε
V = (V+) +( V-) – Ir
V = ε – Ir
According to Ohm’s law, V = IR
IR = ε – Ir
ε = IR + Ir
ε = I(R + r)
Emf formula
Electromotive force is the measure of energy per unit charge. Thus, it measures the amount of energy resulting in the flow of current in a circuit.
ε = E/Q
ε = emf of the cell (voltage)
E = energy (joules)
Q = charge (coulombs)
Emf is different from the potential difference. Emf is the amount of energy per unit charge, while the potential difference is energy changed into a different form per unit charge.
Emf metre
Emf metre works on the principle of Faraday’s law of induction. It is also called an electromagnetic flow metre. Emf metre is useful to measure electric field and magnetic field lines. The Emf metre comprises an electromagnetic coil (to generate a magnetic field) and electrodes (to capture emf). Inside the emf metre, an electromotive force is generated inside the pipe due to the moving conductive liquid inside the magnetic field. The induced voltage is directly proportional to the magnetic field, the distance between electrodes, and flow velocity. The induced voltage is perpendicular to the magnetic field and fluid velocity. The voltage increases inside the emf metre with the increase in the flow rate of the conductive fluid. Inside the emf metres, the flow velocity of liquid in the magnetic field is converted into electricity. Readings of the emf metre are not affected by changes in temperature, pressure, or viscosity of the liquid.
Potentiometer – Comparison of emf
The potentiometer is a versatile instrument made up of a uniform wire connected across a standard cell. It is useful to measure the emf of a cell and also in comparing the emf of two cells. What comes as a bonus is the use of a potentiometer to measure the internal resistance of a cell. A potentiometer doesn’t draw current from the voltage source (cell). Thus, it is not affected by the internal resistance of a cell. A potentiometer is prepared from a material with high resistivity and low-temperature coefficient. After stretching the wires on a wooden board, they are joined in series with the help of thick copper strips.
When constant current flows through the wires of the potentiometer of the unit cross-sectional area, the potential difference between the two points is directly proportional to the length of the wire.
One application of the potentiometer is to compare the emf of two cells, ε1 and ε2.
1, 2, and 3 form a two-way key. When 1 and 3 are connected, the galvanometer is connected to ε1 and when 2 and 3 are connected, it is connected to ε2.
On moving the jockey around distance l1 from A to N1, you will not observe any deflection in the reading of the galvanometer. Under such conditions, according to Kirchoff’s law:
φ l 1 + 0 – ε1 = 0———(1)
On balancing ε2 against length l2
φ l 2 + 0 – ε2 = 0———(2)
On dividing equations 1 and 2:
ε1/ε2 = l 1/l 2
Choose one of the cells as a standard cell with a known emf. Thus it becomes easy to find
the emf of another cell.
What is back emf?
Due to the change in magnetic flux across a single isolated coil, an emf is induced in it. This self-induced emf is also called back emf. Back emf resists increase or decrease of current in the coil. Thus, the back emf works as inertia. To allow the flow of current through the circuit, work is done against back emf. Back emf or induced emf of a coil depends upon the geometry and permeability of the medium.
L = NΦB/I
L = back emf or self-inductance
N = number of turns in the coil
ΦΒ = Magnetic flux
I = Current
Conclusion
Emf of a cell is the total potential difference between the two electrodes. The potentiometer doesn’t draw current from the source of voltage. It is used to measure the internal resistance of a cell and to compare two emf. Back emf or induced emf resists the change in current in an electric circuit. This back emf is responsible for voltage drop when the motor rotates.
