Contents
Physics Topics can also be used to explain the behavior of complex systems, such as the stock market or the dynamics of traffic flow.
What is a Transformer? What do you Mean by the Efficiency of a Transformer?
The electrical appliance used to increase or decrease alternating voltage, is called a transformer. The transformer, which increases the voltage is called a step-up transformer, and the transformer used to decrease the voltage is called a step-down transformer.
Transformer works on the principle of mutual induction between a pair of coils.
Description :
The core of a transformer is constructed by a number of thin laminated sheets of soft iron placed one over the other. It is known as laminated core. A core of a special shape is so chosen that no part of the magnetic flux is wasted and hence the density of lines of induction inside the core becomes maximum. Two insulated wires are wound in many turns [Fig.] on the middle arm of the core very close to each other.
One coil acts as the primary (P) and the other as the secondary (S).
Working principle:
An alternating voltage (Vp) is applied to the primary coil from an alternating current source. The alternating current in the coil P generates induced emf in the secondary coil S, i.e., an alternating voltage Vs is generated between the ends of S. If the dissipation of magnetic flux and loss of energy due to heating be neglected in this transformer (called an ideal transformer), it can be proved that,
\(\frac{V_s}{V_p}\) = \(\frac{N_s}{N_p}\) = k
where Np and Ns are the total number of turns of the primary and secondary coils, respectively, k is called the turns ratio or transformer ratio.
Because of the special nature of the winding, it can be assumed fairly correctly that the magnetic flux ϕB associated with each turn of primary and secondary is the same. If e is the induced emf in each turn, e = \(-\frac{d \phi_B}{d t}\). Hence the emf induced in the pri-mary coil Vp = Npe = -Np\(\frac{d \phi_B}{d t}\). Similarly, Vs = -Ns\(\frac{d \phi_B}{d t}\). Now, the emf induced in the primary must necessarily be equal to the voltage applied. Then, by dividing the two, \(\frac{V_s}{V_p}\) = \(\frac{N_s}{N_p}\) = k.
- If Ns > Np, i.e., k > 1, Vs > Vp and we get a step-up transformer.
- If Ns < Np, i.e., k < 1, Vs < Vp and we get a step-down transformer.
Uses:
Transformers are widely used in our daily life. With its help a high voltage can be converted into a low voltage and vice versa, whenever necessary. For example,
1. an electrical power station uses step-up transformer to produce and transmit large amount of ac electrical energy over long distances. The energy is transmitted at high voltage (such as 66000V- 132000 V) to reduce the loss of energy due to heating. But supply to domestic area needs low voltages (such as 110 V- 440 V). Such conversions of voltage at different levels are facilitated by step-down transformers.
2. Radio, television, electric bell and other electrical appliances require small-sized transformers.
Energy loss in transformer: In an ideal transformer, power dissipated in primary coil (IpVp) = power dissipated in secondary coil (IsVs) .
But no transformer, in practice, is ideal. Generally, some input energy is wasted in any transformer and hence VsIs < VpIp. The term VsIs/ VpIp is called the efficiency of a transformer.
The main causes of energy loss and their remedies are given below.
i) Copper loss: Generally copper wire is used to make primary and secondary coils. Due to Joule’s heating some energy is wasted as heat energy.
Remedies: Thick wire should be used to reduce this loss of energy.
ii) Iron loss: Iron core should be used in primary and secondary coils.
1. Due to eddy current in this core, energy loss is unavoidable.
Remedies: To reduce such loss, laminated core is used.
2. The change of magnetisation cycle in the core fails to synchronise with ac and some energy is necessarily wasted in the core—known as hysterisis loss.
Remedies: Due to high coercivity, core should not be made of steel. Iron core is more effective in reducing energy loss.
iii) Loss due to magnetic flux leakage: The flux generated by the primary coil may not be wholly linked to the secondary coil due to possible defective design of the core.
Remedies: Obviously, special care should be taken in the construction of the core.
Classification of transformer:
The two most common designs of transformer are given below:
i) Core-type transformer: In this type, primary and secondary coils are wound around the core ring [Fig.(a)]. Here each and every limb is occupied with both primary and secondary winding placed successively around them.
ii) Shell-type transformer: Here the primary and secondary windings pass inside the steel magnetic circuit (core) which forms a shell around the windings [Fig.(b)], The main frame is constructed with three limbs. Both the primary and secondary windings are wound around the central limb.
Besides these, transformers can be classified based on its uses and these are audio frequency transformer, radio frequency transformer, etc.
Numerical Examples
Example 1.
The number of turns in the primary and secondary coils of an ideal transformer are 140 and 280, respectively. If the current through the primary coil is 4 A, what will be the current in the secondary coil?
Solution:
In an ideal transformer, the powers of the secondary and primary coils are equal,
i.e., VsIs = VpIp
∴ Is = Ip ᐧ \(\frac{N_p}{N_s}\) = 4 × \(\frac{140}{280}\) = 2 A.
Example 2.
Initial voltage and input power of a transformer of efficiency 80% are 100 V and 4 kW, respectively. If the voltage of the secondary coil is 200 V, determine the currents flowing through the primary and the secondary coils.
Solution:
Power of the primary coil i.e., input power,
Pp = VpIp
or Ip = \(\frac{P_p}{V_p}\) = \(\frac{4 \times 1000}{100}\) = 40 A
Power of the secondary coil, Ps = Pp × \(\frac{80}{100}\)
Again, Ps = VsIs
So, Is = \(\frac{P_s}{V_s}\) = \(\frac{80}{100} \times \frac{P_p}{V_s}\) = \(\frac{80}{100} \times \frac{4 \times 1000}{200}\) = 16 A.