(a) Explain mutual induction (b) State four use of electromagnets The diagram above illustrates two coils X an arranged so that their axes are collinear. X ...

(a) Mutual induction is the production of an e.m.f. in one coil or circuit when the current in a nearby coil or circuit is changing. The changing current produces a changing magnetic flux which links the second coil.

(b) Uses of electromagnets

1. Electric bells.
2. Electromagnetic relays and switches.
3. Electromagnetic cranes for lifting iron and steel.
4. Magnetic separation of iron scraps from non-magnetic materials.

(c)

1. The alternating current in coil X produces a continuously changing magnetic flux. Some of this flux links coil Y and induces an alternating e.m.f. in it. A current therefore flows through the lamp and it lights.
2. When the coils are brought closer, more of the magnetic flux from X links coil Y. The induced e.m.f. and current in Y increase, so the lamp becomes brighter.
3. The bundle of insulated soft-iron wires has high magnetic permeability and provides a path that concentrates the magnetic flux through both coils. The flux linkage and induced e.m.f. in Y increase, producing a larger current and a brighter lamp. The wires are insulated to reduce eddy currents.

(d)(i) Circuit diagram

(d)(ii) Current through the \(5\,\Omega\) resistor

Since the two cells have equal e.m.f.s and are connected in parallel, the resultant e.m.f. is

\[E = 2.0\text{ V}\]

The equivalent internal resistance is

\[ \frac{1}{r}=\frac{1}{0.4}+\frac{1}{0.1}=2.5+10=12.5 \]

\[ r=\frac{1}{12.5}=0.08\,\Omega \]

Total resistance of the circuit:

\[ R_{\text{total}}=5.0+0.08=5.08\,\Omega \]

Hence,

\[ I=\frac{E}{R_{\text{total}}}=\frac{2.0}{5.08}=0.394\text{ A} \]

Current through the \(5\,\Omega\) resistor \(=0.39\text{ A}\) (approximately).