# Objective Questions on Circuit Theory | Page – 5

1. Link In network theory refers to

B = Branch, N = Nodes, Twig = N -1.
Link, L = B -( N - 1) = B - N + 1.
Link / chord is the branch of a graph that does not belong to the particular tree. It is simply called a link.

2. The voltage across R and L in a series RL circuit are found to be 200 V and 150 V respectively the rms value of the voltage across the series combination is ___ V.

V = √( VR2 + VL2) = √( 2002 + 150 2 ) = 250 V.

3. Whenever electric current is supplied by a source its terminal voltage

Whenever electric current is supplied by a source, this electric current also flows through the internal resistance connected in series in the source. Because of voltage drop across the internal resistance, the terminal voltage is decreased.

4. A electric current of 4 A flows in an ac circuit when 100 v dc is applied to it whereas it takes 250 v ac to produce the same electric current the power factor of the circuit is

With dc R = V / I = 100 / 4 = 25 ohms
With ac Z = V / I = 250 / 4 = 62.5 ohms.
∴ cos φ = R / Z = 25 / 62.5 = 0.4.

5. Which of the following cannot be connected in series unless they are identical?

Current source cannot be connected in series unless identical because in series all individual current sources have same values.

6. A reactance having an inductor of 0.15 H is connected in series with 10 ohm resistance. What will be the inductive reactance?

Inductive reactance XL = 2πfL = 2 × 3.14 × 50 × 0.15 = 47.1 Ω

7. Kirchhoff's second law is based on law of conservation of

Kirchhoff's voltage law (KVL) is also called Kirchhoff's second law. The principle of conservation of energy implies that the directed sum of the electrical potential differences (voltage) around any closed network is zero.

8. A series circuit consists of R = 20 Ω, L = 20 mH, and ac supply 60 V with f = 100 Hz. The electric current in R is

The expression for impedance of series R - L circuit is Z = ( R2 + 4.π2f2L2)1 / 2
Here, R = 20 Ω, L = 20 mH, V = 60 V and f = 100 Hz
Z = [202 + 4 × 3.142 × 100 2 × (20 × 10 - 3)2]1 / 2 = 23.61 Ω
Therefore, electric current through the circuit i.e both through resistor and inductor will be 60 / 23.61 = 2.54 A.

9. A series circuit consists of R = 20 Ω, L = 20 mH, and ac supply 60 V with f = 100 Hz. The voltage drop across R is

The expression for impedance of series R - L circuit is Z = (R2 + 4.π2f2L2)1 / 2
Here, R = 20 Ω, L = 20 mH, V = 60 V and f = 100 Hz
Z = [202 + 4 × 3.142 × 1002 × (20 × 10- 3)2 ]1 / 2 = 23.61 Ω
Therefore, electric current through the circuit i.e both through resistor and inductor will be 60 / 23.61 = 2.54 A
The voltage drop across R is V = IR = 2.54 × 20 V = 50.8 V.

10. A series circuit consists of R = 20 Ω, L = 20 mH, and ac supply 60 V with f = 100 Hz. The voltage drop across L is

The expression for impedance of series R - L circuit is Z = (R2 + 4&pi2f2L2)1 / 2
Here, R = 20 Ω, L = 20 mH, V = 60 V and f = 100 Hz
Z = [202 + 4 × 3.142 × 1002 × ( 20 × 10 - 3 )2]1 / 2 = 23.61 Ω
The reactance of the circuit, X = 2πfL = 2 × 3.14 × 100 × 20 × 10 - 3 = 12.56 Ω
Electric current through the circuit i.e both through resistor and inductor will be 60 / 23.61 = 2.54 A
Voltage drop across L is XI = 12.56 × 2.54 = 31.9 V.

11. A series circuit consists of R = 20 Ω, L = 20 mH, and ac supply 60 V with f = 100 Hz. The phase angle of electric current in respect of supply voltage will be

The expression for impedance of series R - L circuit is Z = (R2 + 4.π2.f2.L2)½
Here, R = 20 Ω, L = 20 mH, V = 60 V and f = 100 Hz
Z = [202 + 4 × 3.142 × 100 2 × (20 × 10 - 3)2]1 / 2 = 23.61 Ω
The reactance of the circuit, X = 2πfL = 2 × 3.14 × 100 × 20 × 10 - 3 = 12.56 Ω
∴ The phase angle of electric current in respect of supply voltage will be θ = sin - 1(X/Z) = sin - 1(12.56 / 23.61) = 32.1°.

12. If a resistor and an inductor are connected in series across a voltage source. Which two parameters in that circuit increase if frequency of voltage source increases?

If frequency of the voltage source increases, the reactance of the inductor increases as because XL = 2πfL and if XL and that causes increase in the total impedance Z, of the circuit, which results decreasing the electric current I through the circuit. If electric current is reduced, the voltage drop across the resistor VR is decreased. Again voltage drop across the inductor is the difference of supply voltage and voltage drop across the resistor, hence voltage across inductor VL will increase.

13. If a resistor and an inductor are connected in series across a voltage source . Which two parameters in that circuit decrease if frequency of voltage source increases?

If frequency of the voltage source increases, the reactance of the inductor increases as because XL = 2πfL and if XL and that causes increase in the total impedance Z, of the circuit, which results decreasing the electric current I through the circuit. If electric current is reduced, the voltage drop across the resistor VR is decreased. Again voltage drop across the inductor is the difference of supply voltage and voltage drop across the resistor, hence voltage across inductor VL will increase.

14. If a resistor and a capacitor are connected to form series R - C circuit across a voltage source . If frequency of voltage source increases

In series RC circuit if supply frequency is increased, the electric current increases. Because the impedance of capacitor is ..........That is capacitive impedance is inversely proportional to frequency. As capacitive impedance decreases with increase in frequency, the overall impedance of the series RC circuit is decreased which results increase in electric current through the circuit.

15. A branch of a network is said to be active when it consists of one

When a branch of a network contains one or more sources it is called an active branch.

16. A branch of a network is said to be passive when it contains

A branch that does not contain any source is known as a passive branch. Voltmeter is not a source.

17. Which of the following is not a bilateral?

A bilateral element conduct equally well in either directions. Such as resistor & inductor. When the electric current voltage relation are different for the two directions of electric current flow, the element is said to be unilateral. Diode is a unilateral element.

18. Which of the following characteristics is attributed to an ideal independent voltage source ?

In independent ideal voltage source is such a source, which gives fixed voltage, irrespective of magnitude and direction of electric current flowing through it.

19. Dependent source of electric current and voltage are those which have,

The source whose output voltage or electric current is a function of the voltage or electric current in another part of the circuit is called dependent source.

20. The internal resistance of a practical voltage source is considered to be connected in

Whenever load is connected to the voltage source , its terminal voltage decreases become of its internal resistance. Hence the internal resistance of a practical voltage source is assumed to be connected in series with the source.