Electric Circuit Analysis Concept and MCQ

PHASOR ALGEBRA-

To represent R, XL, XC in rectangular form:

ZR = R + j0

ZL = 0 + j XL

ZC = 0 - jXC

To represent R, XL, XC in polar form :

ZR =R ∠ 0°

ZL = XL ∠ 90°

ZC = XC ∠ -90°

Circuit response of single elements for DC:-

Voltage across each element for i = Im sin ωt → I = |I| ∠20°

Current through each element when v = Vm sin ωt → V = V∠0°

1. A phasor represents:

(A) A sinusoidal quantity having amplitude only
(B) A sinusoidal quantity having both magnitude and phase
(C) A DC quantity
(D) A random signal

✅ Answer: (B) A sinusoidal quantity having both magnitude and phase

🧠 Explanation:
A phasor is a vector representation of a sinusoidal quantity (like voltage or current). It shows the amplitude (magnitude) and the phase angle with respect to a reference.
Example: $V = V_m ∠θ$

2. The phasor representation of $v(t) = 100 \sin(ωt + 30°)$ is:

(A) 100 ∠0°
(B) 100 ∠30°
(C) 70.7 ∠30°
(D) 50 ∠60°

✅ Answer: (B) 100 ∠30°

🧠 Explanation:
The phasor form of a sinusoidal voltage is written as $V = V_m ∠θ$ , where $V_m$ is the amplitude and $θ$ is the phase angle.
Hence, for $v(t) = 100 \sin(ωt + 30°)$ , the phasor is $100∠30°$ .

3. If two phasors are 90° apart, then their vector sum will be:

(A) Arithmetic sum
(B) Geometric sum
(C) Vector (phasor) sum using Pythagoras
(D) Zero

✅ Answer: (C) Vector (phasor) sum using Pythagoras

🧠 Explanation:
When two phasors are 90° apart, they are perpendicular.
Resultant $R = \sqrt{A^2 + B^2}$

Example:
If A = 3∠0°, B = 4∠90°,
then R = √(3² + 4²) = 5.

4. The complex representation of a phasor $V = V_m∠θ$ is:

(A) $V_m e^{jθ}$
(B) $V_m \sin(θ)$
(C) $V_m \cos(θ)$
(D) $V_m \tan(θ)$

✅ Answer: (A) $V_m e^{jθ}$

🧠 Explanation:
Using Euler’s formula,
$e^{jθ} = \cosθ + j\sinθ$ .
Hence, the complex form of a phasor is $V = V_m e^{jθ}$ , which can also be written as $V = V_m(\cosθ + j\sinθ)$ .

5. The phasor sum of $10∠0°$ and $10∠180°$ is:

(A) 20∠0°
(B) 10∠90°
(C) 0
(D) 20∠180°

✅ Answer: (C) 0

🧠 Explanation:
The two phasors are equal in magnitude but opposite in phase.
So they cancel each other:
$10∠0° + 10∠180° = 0$ .

6. The resultant of $5∠0°$ and $5∠90°$ is:

(A) 5
(B) 7.07
(C) 10
(D) 2.5

✅ Answer: (B) 7.07

🧠 Explanation:
Resultant $R = \sqrt{5^2 + 5^2} = \sqrt{50} = 7.07$ .
Since the phasors are at right angles (0° and 90°), we use Pythagoras theorem.

7. In phasor algebra, addition of phasors is done by:

(A) Direct arithmetic addition
(B) Vector addition
(C) Subtraction of magnitudes
(D) Simple multiplication

✅ Answer: (B) Vector addition

🧠 Explanation:
Phasors represent vectors. Therefore, their addition follows vector laws of addition, considering both magnitude and phase angle.

8. If $I_1 = 4∠0°$ and $I_2 = 3∠180°$ , resultant current = ?

(A) 7 A
(B) 1 A
(C) 5 A
(D) 12 A

✅ Answer: (B) 1 A

🧠 Explanation:
Since both are in opposite phase,
$I = |I_1 - I_2| = |4 - 3| = 1 A$ .

9. The angle between voltage and current phasor in a pure inductor is:

(A) 0°
(B) 90° (Voltage leads current)
(C) 90° (Current leads voltage)
(D) 180°

✅ Answer: (B) 90° (Voltage leads current)

🧠 Explanation:
In a pure inductor, current lags voltage by 90°, so voltage leads current by 90°.

10. If $V = 230∠0°$ and $I = 10∠-30°$ , the phase difference between voltage and current is:

(A) 0°
(B) 30°
(C) 60°
(D) 90°

✅ Answer: (B) 30°

🧠 Explanation:
Voltage leads current by 30°, since current’s phase angle is -30° relative to voltage (0°).

INDEPENDENT AND DEPENDENT SOURCES:-

(i) Voltage-controlled voltage source (VCVS). Eg. Operational amplifier

(ii) Voltage controlled current source (VCCS). Eg. Field effect transistor

(iii) Current-controlled voltage source (CCVS).

(iv) Current-controlled current source (CCCS). Eg. Common base transistor

1. An independent voltage source maintains:

(A) Constant voltage irrespective of current
(B) Constant current irrespective of voltage
(C) Both voltage and current constant
(D) Zero voltage always

✅ Answer: (A) Constant voltage irrespective of current

🧠 Explanation:
An independent voltage source supplies a fixed voltage even if the load current changes.
Example: A 12 V battery always maintains 12 V across its terminals.

2. An independent current source maintains:

(A) Constant current regardless of voltage
(B) Constant voltage regardless of current
(C) Variable current depending on resistance
(D) Zero current always

✅ Answer: (A) Constant current regardless of voltage

🧠 Explanation:
An independent current source provides a constant current no matter how the terminal voltage changes due to load variations.

3. The symbol of a dependent source has:

(A) A diamond shape
(B) A circle
(C) A rectangle
(D) A triangle

✅ Answer: (A) A diamond shape

🧠 Explanation:
In circuit diagrams:

Independent sources → shown by circle
Dependent sources → shown by diamond (rhombus)

4. A dependent (controlled) source is one whose value depends on:

(A) External environmental conditions
(B) Another voltage or current elsewhere in the circuit
(C) Frequency of supply only
(D) Type of material used

✅ Answer: (B) Another voltage or current elsewhere in the circuit

🧠 Explanation:
A dependent source provides voltage or current that is controlled by another voltage or current in the same circuit.

5. How many types of dependent sources are there?

(A) Two
(B) Three
(C) Four
(D) Five

✅ Answer: (C) Four

🧠 Explanation:
There are 4 types of dependent sources:

Voltage Controlled Voltage Source (VCVS)
Current Controlled Voltage Source (CCVS)
Voltage Controlled Current Source (VCCS)
Current Controlled Current Source (CCCS)

6. In a Voltage Controlled Voltage Source (VCVS), the output voltage depends on:

(A) An input voltage elsewhere in the circuit
(B) An input current elsewhere
(C) Its own internal resistance
(D) Supply frequency

✅ Answer: (A) An input voltage elsewhere in the circuit

🧠 Explanation:
In VCVS, output voltage $V_{out} = kV_x$ ,
where $V_x$ is some controlling voltage in the circuit.

7. In a Current Controlled Voltage Source (CCVS), the output voltage is proportional to:

(A) A controlling current
(B) A controlling voltage
(C) Resistance
(D) Power

✅ Answer: (A) A controlling current

🧠 Explanation:
For CCVS, output voltage $V_{out} = rI_x$ ,
where $I_x$ is the controlling current and $r$ is a proportional constant (transresistance).

8. A Voltage Controlled Current Source (VCCS) produces:

(A) Output current depending on input voltage
(B) Output voltage depending on input current
(C) Constant voltage
(D) Constant power

✅ Answer: (A) Output current depending on input voltage

🧠 Explanation:
For VCCS, $I_{out} = gV_x$ ,
where $g$ is the transconductance and $V_x$ is the controlling voltage.

9. A Current Controlled Current Source (CCCS) produces:

(A) Output current proportional to another current in the circuit
(B) Output voltage proportional to another voltage
(C) Constant voltage output
(D) No output

✅ Answer: (A) Output current proportional to another current in the circuit

🧠 Explanation:
For CCCS, $I_{out} = βI_x$ ,
where $I_x$ is controlling current and $β$ is a constant (current gain).

10. In circuit analysis, dependent sources are used to model:

(A) Real-world devices like transistors and amplifiers
(B) Only resistors
(C) Ideal capacitors
(D) DC batteries

✅ Answer: (A) Real-world devices like transistors and amplifiers

🧠 Explanation:
Dependent sources represent controlled devices —
like BJTs, MOSFETs, and operational amplifiers, where the output depends on an input signal.

11. The unit of transconductance (g) in VCCS is:

(A) Ω (Ohm)
(B) Siemens (S)
(C) Volt (V)
(D) Ampere (A)

✅ Answer: (B) Siemens (S)

🧠 Explanation:
In VCCS, $I = gV$ .
So, $g = \frac{I}{V}$ .
Unit of current/voltage = A/V = Siemens (S).

12. For a dependent source $V = 5I_x$ , it is a:

(A) Voltage Controlled Voltage Source
(B) Current Controlled Voltage Source
(C) Voltage Controlled Current Source
(D) Current Controlled Current Source

✅ Answer: (B) Current Controlled Voltage Source

🧠 Explanation:
The output is voltage (V) and it depends on current (I_x) → CCVS type.

13. If a dependent source has output current $I = 2V_x$ , it is:

(A) Voltage Controlled Current Source (VCCS)**
(B) Current Controlled Current Source (CCCS)**
(C) Voltage Controlled Voltage Source (VCVS)**
(D) Current Controlled Voltage Source (CCVS)**

✅ Answer: (A) Voltage Controlled Current Source (VCCS)**

🧠 Explanation:
Since output is current, and it depends on voltage, it’s a VCCS.

14. In the symbol of a dependent source, the controlling variable is shown by:

(A) A small arrow and label near the symbol**
(B) A resistor symbol**
(C) A battery symbol**
(D) A dot mark**

✅ Answer: (A) A small arrow and label near the symbol

🧠 Explanation:
Dependent sources are labeled with the controlling variable (like $V_x$ or $I_x$ ) next to the diamond symbol to indicate dependency.

15. The Norton equivalent circuit uses:

(A) Current source in parallel with resistance
(B) Voltage source in series with resistance
(C) Dependent source in series with capacitor
(D) Both (A) and (B)

✅ Answer: (A) Current source in parallel with resistance

🧠 Explanation:
Norton’s theorem represents any linear circuit as an independent current source in parallel with a resistance (called Norton resistance).