APPLIED ELECTRICITY
Q1. Find currents and voltages in the circuit shown in Fig. Q1.
Solution:
Q2. Determine the voltages at the nodes in Fig. Q2.
Solution:
Q3a. Find io in the circuit of Fig. Q3 using superposition.
Solution:
Q3b. Using Norton’s theorem, find RN and IN of the circuit in Fig. Q3b at terminals a-b.
Solution:
Q4a. Find the Thevenin equivalent of the circuit in Fig. Q4a at terminals a-b.
Solution:
Q4a. Find the Thevenin equivalent of the circuit in Fig. Q4a at terminals a-b.
Q5a. A waxed paper capacitor has two parallel plates, each of effective area 800 cm2. If the capacitance
of the capacitor is 4425 pF determine the effective thickness of the paper if its relative permittivity is 2.5
Solution:
Q5b. Capacitance of 1µF, 3µF, 5µF, and 6µF are connected in parallel to a direct voltage supply of 100 V.
Determine (a) the equivalent circuit capacitance, (b) the total charge and (c) the charge on each
capacitor.
Solution:
Q6a. The flux density between two plates separated by mica of relative permittivity 5 is 2µC/m2. Find
the voltage gradient between the plates.
Solution:
Q6b A section through a magnetic circuit of uniform cross-sectional area 2 cm2 is shown in figure Q6b.
The cast steel core has a mean length of 25 cm. The air gap is 1 mm wide and the coil has 5000 turns.
The B-H curve for cast steel, Shows that when B = 0.8T, H = 750A/m. Determine the current in the coil to
produce a flux density of 0.80T in the air gap, assuming that all the Flux passes through both parts of the
magnetic circuit.
Solution:
Q7a. Can a magnetic field be setup by electric current? Explain a simple experiment to prove your
answer.
Solution:
Let a piece of wire be arranged to pass vertically through a horizontal sheet of cardboard on which is
placed some iron filings, as shown in Fig. 10.1(a). If a current is now passed through the wire, then the
iron filings will form a definite circular field pattern with the wire at the centre when the cardboard is
gently tapped. By placing a compass in different positions the lines of flux are seen to have a definite
direction, as shown in Fig. 10.1(b).
If the current direction is reversed, the direction of the lines of flux is also reversed. The effect on both
the iron filings and the compass needle disappears when the current is switched off. The magnetic field
is thus produced by the electric current. The magnetic flux produced has the same properties as the flux
produced by a permanent magnet. If the current is increased the strength of the field increases and, as
for the permanent magnet, the field strength decreases as we move away from the current-carrying
conductor.
In Fig. 10.1, the effect of only a small part of the magnetic field is shown. If the whole length of the
conductor is similarly investigated it is found that the magnetic field round a straight conductor is in the
form of concentric cylinders, as shown in Fig. 10.2, the field direction depending on the direction of the
current flow.
When dealing with magnetic fields formed by electric current it is usual to portray the effect as shown in
Fig. 10.3. The convention adopted is:
(i) Current flowing away from the viewer, i.e. into the paper, is indicated by ⊕. This may be thought of
as the feathered end of the shaft of an arrow. See Fig. 10.3(a).
(ii) Current flowing towards the viewer, i.e. out of the paper, is indicated by. This may be thought of as
the point of an arrow. See Fig. 10.3(b).
Q7b. Why solenoid is important in electromagnetic theory. Give four examples of electrical experiments
that it is used.
Solution:
The solenoid is very important in electromagnetic theory since the magnetic field inside the solenoid is
practically uniform for a particular current, and is also versatile, inasmuch that a variation of the current
can alter the strength of the magnetic field. An electromagnet, based on the solenoid, provides the basis
of many items of electrical equipment, examples of which include electric bells, relays, lifting magnets
and telephone receivers.
Q7c. Differentiate between self and mutual inductance.
Self-inductance is the characteristic of the coil itself. Mutual inductance is the characteristic of a pair of
coil.