Question

a) State the principle of a transformer. Explain its construction and working. Derive an expression for the ratio of e.m.f’s in terms of number of turns in primary and secondary coil.
b) Two diametrically opposite points of a metal ring are connected to two terminals of the left gap of Meter Bridge. The resistance of $11\Omega$ is connected in the right gap. If a null point is obtained at a distance of $45cm$ from the left end, find the resistance of the metal ring.

Answer 1

a) Transformer is an electrical device that converts AC electrical energy from one circuit to another circuit. This transfer of energy takes place at a constant frequency.
b) Meter bridge is a metal bridge that is based on the principle of Wheatstone bridge and it is used to find the value of unknown resistance.

Complete Step-by-step Solution:
a) Transformer is a device that is used only to transfer electrical energy from one circuit to another. It is not a machine but an electrical device.
Transformer is based on the principle of electromagnetic induction. In a transformer there exists mutual inductance between two circuits and they are linked by a common mutual flux. The transformer consists of two coils which are electrically separated but magnetically linked.
Transformer has two coils for mutual inductance and has a laminated steel core. The coils are electrically separated but magnetically linked. It is kept in a container for core and windings and it is kept in an insulated oil.
We know that the EMF equation of transformer is given by :
Let us consider ${N_1}$ be the number of turns in primary and ${N_2}$be the number of turns in secondary
According to Faraday’s law of electromagnetism, EMF induced be ${e_1}$and${e_2}$.
${e_1} = - {N_1}\dfrac{{d\phi }}{{dt}}$ and ${e_2} = - {N_2}\dfrac{{d\phi }}{{dt}}$
Let us consider flux be given by the function:
$\phi = {\varphi _m}\sin \omega t$
Putting this value in the above equation:
${e_1} = - {N_1}\omega {\phi _m}\cos \omega t$ and ${e_2} = - {N_2}\omega {\phi _m}\cos \omega t$
Rms value of EMF, ${E_2}$induced in secondary winding is:
${E_2} = \dfrac{{{E_2}}}{{\sqrt 2 }} = \sqrt 2 \pi f{N_2}{\phi _m}$ and ${E_1} = \dfrac{{{E_1}}}{{\sqrt 2 }} = \sqrt 2 \pi f{N_1}{\phi _m}$
Maximum value is obtained when $\sin (\omega t - \dfrac{\pi }{2})$ is $1$.
Now, taking the ratio of ${E_1}$ and ${E_2}$, we get:
$\dfrac{{{E_1}}}{{{E_2}}} = \dfrac{{{N_1}}}{{{N_2}}} = \sqrt 2 \pi f{\phi _m}$
This is the required expression.
b) From the Wheatstone bridge principle, we know:
$\dfrac{P}{Q} = \dfrac{R}{S}$
Resistance per length of the wire be $p$
Null point is at$45cm$,
Putting the values of resistance:
$P = 45p$
$Q = 55p$
$R = 11\Omega$
Thus, putting the value, we get:
$\dfrac{{45p}}{{55p}} = \dfrac{{11}}{S}$
Thus, we obtain:
$S = 13.44\Omega$
This is the required solution.

Note:
Transformer is a device that only operates on AC and not on DC. This is because DC does not produce alternating flux and neither does it cause change in flux linkages. Thus the process of electromagnetic phenomenon does not take place, with DC source.