Network Theory Questions and Answers Part-1

1. Energy per unit charge is ____________
a) Power
b) Voltage
c) Current
d) Capacitance

Answer: b
Explanation: The work or energy per unit charge utilised in the process of separation of charges is known as Voltage or Potential difference. The phenomenon of transfer of charge from one point to another is termed Current. The rate at which the work is done is called Power. Charge per unit voltage is Capacitance.

2. A conductor is said to have resistance of one ohm if a potential difference of one volt across its terminals causes a current of X ampere to flow through it. What will be the value of X?
a) 4
b) 2
c) 3
d) 1

Answer: d
Explanation: Ohm’s law states that the potential difference (voltage) across a conductor is proportional to the current through it. The constant of proportionality is called the Resistance(R).
According to Ohm’s law, V = IR (where V is the potential difference between two points which include a resistance R).
–> I = V/R = 1V/1Ω = 1A.

3. Resistance depends on the temperature of the conductor.
a) True
b) False

Answer: a
Explanation: Resistance is directly proportional to its length, inversely proportional to the area of cross section of the conductor, depends on the nature of the material and on the temperature of the conductor.

4. A 25 Ω resistor has a voltage of 150 sin377 t. Find the corresponding power.
a) 900 sin2 337 t
b) 90 sin2 337 t
c) 900 sin2 377 t
d) 9 sin2 337 t

Answer: c
Explanation: Given R = 25 Ω and v = 150 sin 377 t
i = \(\frac{v}{R} = \frac{150 sin⁡ 377 t}{25}\) = 6 sin 377 t
p = vi = (150 sin 377 t)(6 sin 377 t) = 900 sin2 377 t.

5. Unit of inductance is ________
a) Weber
b) Henry
c) Farad
d) Tesla

Answer: b
Explanation: The unit of inductance is Henry. Weber is the unit of magnetic flux. Tesla is the unit of flux density. Farad is the unit of capacitance.

6. Inductance of an inductor is inversely proportional to its ___________
a) Number of turns
b) Area of cross section
c) Absolute permeability
d) Length

Answer: d
Explanation: Inductance of an inductor, L = µN2A/l
From the above equation, Inductance of an inductor is inversely proportional to its length.

7. Energy stored in an inductor is ________
a) LI
b) LI2
c) LI/2
d) LI2/2

Answer: d
Explanation: V = L \(\frac{di}{dt}\)
dE = Vidt = L \(\frac{di}{dt} idt\) = Lidt
E = \(\int_0^I dE = \int_0^I Lidt = \frac{1}{2} LI^2\).

8. An inductor of 3mH has a current i = 5(1 – e-5000t). Find the corresponding maximum energy stored.
a) 37.5 mJ
b) 375 J
c) 37.5 kJ
d) 3.75 mJ

Answer: a
Explanation: Given L = 3 mH, i = 5(1 – e-5000t)
V = L \(\frac{di}{dt} = 3 × 10^{-3} \frac{d}{dt}[5(1-e^{-5000t})] = 75 e^{-5000t}\)
I = i(∞) = 5(1 – e-∞) = 5 A
E = \(\frac{1}{2}\) LI2 = 0.5 × 3 × 10-3 × 52 = 37.5 mJ.

9. The capacitance of a capacitor does not depend on the absolute permittivity of the medium between the plates.
a) True
b) False

Answer: b
Explanation: C = Ɛ \(\frac{A}{d}\)
Where d is the distance between the plates, A is the cross-sectional area of the plates and Ɛ is absolute permittivity of the medium between the plates.
Hence, the capacitance of a capacitor depends on the absolute permittivity of the medium between the plates.

10. Which of the following is not the energy stored in a capacitor?
a) \(\frac{CV^2}{2}\)
b) \(\frac{QV}{2}\)
c) \(\frac{Q^2}{2C}\)
d) \(\frac{QC}{2}\)

Answer: d
Explanation: Energy stored in a capacitor, E = \(\frac{CV^2}{2}\)
Since C = Q/V
E = \(\frac{CV^2}{2} = \frac{QV}{2} = \frac{QC}{2}\).