Basics of Electricity ( Electrical Engineering)

SECTION D

D1. In the circuit shown in Figure D1, all resistors are 8 O, and the internal resistance of
each battery is 3 O. Other parameters are shown on the circuit diagram.
a) Determine the values of the currents that flow through each resistor R1, R2,
R3, and R4. The directions of the current through each resistor should be
indicated by arrows on the circuit diagram.

b) Determine the reading of a voltmeter connected between the points A and B.

c) Determine the amount of charge accumulated on the capacitor C1. What is
the sign of the charge on the left-hand-side plate of the capacitor?

D2. a) A circuit diagram for the unity-gain amplifier, connected between a source
and a load, is shown in Figure D2. Note that the amplifier does not provide
any voltage amplification.
(i) What may be a purpose of using the amplifier between the source and
the load? Which parameters of the amplifier are of importance for
that?
(ii) Can this amplifier provide any kind of amplification?

b) Describe the meaning of the term “earthing” (or “grounding”) for electric
circuits, both in terms of the electric field potential and the capacitance.
Explain why the two descriptions are equivalent.

c) In which two cases the voltage measured between the terminals of a battery
is equal to the EMF of the battery?

d) A metal ball is placed in the electric field. Is there any electric charge induced
(i) inside the volume of the ball; (ii) on its surface? Explain your reasoning.

D3. (a) Six resistors are connected together to form a tetrahedron, their values are
shown in Figure D2. Determine the circuit resistance between points A and
B. Show your working.

(b) A circuit consists of a capacitor C1 = 60 µF and a variable capacitor C2, which
are connected in series. Initially, C2 = 30 µF. The circuit is connected to a
battery of EMF E = 25 V. After that, the value of C2 is changed to 20 µF.
Determine the amount of charge ?Q that will pass through the battery while
C2 is changed. Show your working.

b) Two capacitors have identical geometry (i.e. plate size and distance between
them) but are filled with different dielectric materials. In the 1st capacitor, the
dielectric permittivity of the material is e1 ˜ 1, while in the 2nd capacitor, the
dielectric permittivity is e2 = 4. The capacitors are connected in parallel to a
voltage source; E1 and E2 are the electric field intensities in the 1st and the
2nd capacitors, respectively.
Find the ratio . Show your working.

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