| a. |
A
closed rectangular coil of N turns each of area A is rotated at a constant
angular speed w
in a uniform magnetic field of flux density B. Give an expression for the
e.m.f. x induced
in the coil. With the aid of a diagram, state the position of the coil
when x is
i)
maximum |
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ii)
zero. |
5
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Suppose at time t, the normal of coil makes
an angle q with the field lines. q
= w t.
The magnetic flux linkage is |
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The induced e.m.f. is |
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The induced e.m.f.
x is the largest when wt = 90o.
i.e. when the plane of coil is parallel to the field lines. |
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The induced e.m.f.
x is the smallest when wt = 0o.
i.e. when the plane of coil is at right angles to the field lines. |
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| b. |
Explain
how a transformer works. Indicate the energy losses which occur in the
transformer and explain how they are reduced to the minimum. |
3
marks |
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As an a.c. is applied across the primary coil, the induced
e.m.f. |
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Assuming no flux linkage, the induce e.m.f.
across the secondary is |
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Thus, |
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In practical transformer, energy may be lost in Joule heating
by the coil resistance. The changing flux in the transformer would induce
eddy current in the soft-iron core. This, in turn, would produce heat and
thus power loss. |
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The eddy current may be minimized by using laminated iron
core. |
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| c. |
Describe
the analogous resulting effects when a battery is connected in turn across
circuits consisting of
i)
an inductor and resistor in series, and |
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ii)
an uncharged capacitor and resistor in series.
A full mathematical
analysis is only expected for (i). |
8
marks |
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When the switch in (a) is closed, the current
starts to rises from zero. The maximum steady current is |
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Before the current reaches Io, we have |
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The rise in current is similar to the rise
in charge of a capacitor. |
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