A sinusoidal voltage v(t) = 300sin(100πt) V is applied to a 50 Ω resistor. What is the average power dissipated?
Answer: B
Vm = 300 V, VRMS = 300/√2 = 212.13 V, P = VRMS²/R = (212.13)²/50 = 900 W
Q.22Medium
What is the relationship between source voltage (Vs), terminal voltage (Vt), and current (I) in a real voltage source with internal resistance r?
Answer: A
In a real voltage source, terminal voltage Vt = Vs - Ir, hence Vs = Vt + Ir (accounting for voltage drop across internal resistance)
Q.23Medium
A network has two meshes with currents I₁ = 3A and I₂ = 2A. The mutual inductance between the coils is 0.5H. What is the mutual inductance voltage in the first coil due to current change in the second coil at dI₂/dt = 4 A/s?
Answer: C
Mutual inductance voltage V = M × dI/dt = 0.5 × 4 = 2V
Q.24Medium
A parallel RC circuit is connected to a 100V AC source at 50Hz. If R = 20Ω and C = 100μF, what is the total impedance of the circuit?
Answer: A
For parallel RC: Xc = 1/(2πfC) = 1/(2π×50×100×10⁻⁶) = 31.83Ω. Z = (R×Xc)/√(R²+Xc²) = (20×31.83)/√(400+1013) ≈ 15.8Ω
Q.25Medium
In mesh current analysis for a two-mesh circuit with self-resistances R₁ = 10Ω, R₂ = 15Ω and mutual resistance Rm = 5Ω, and voltages V₁ = 20V, V₂ = 0V, what would be the mesh impedance matrix determinant?
In delta-to-star transformation, if delta resistances are Ra = 30Ω, Rb = 40Ω, Rc = 50Ω, what is the star resistance R₁ (connected to point corresponding to Ra)?
What is the reactive power in an AC circuit with apparent power S = 1000VA and power factor = 0.8?
Answer: B
P = S × PF = 1000 × 0.8 = 800W. Q = √(S² - P²) = √(1000000 - 640000) = √360000 = 600 VAR
Q.29Medium
A network has 8 branches and 5 nodes. The number of independent mesh equations required is:
Answer: B
Number of independent mesh equations = b - n + 1, where b=branches, n=nodes. Here: 8 - 5 + 1 = 4
Q.30Medium
For maximum power transfer to a load from a source with Thevenin equivalent (Vth, Rth), the load resistance should be:
Answer: C
Maximum power transfer theorem: Load resistance RL should equal Thevenin resistance Rth for maximum power delivery. Maximum power = Vth²/(4Rth)
Q.31Medium
In a planar circuit, the relationship between number of nodes (n), branches (b), and independent loops (m) is:
Answer: B
For a connected planar circuit: Number of independent loops = b - n + 1 (also known as cyclomatic complexity or mesh rank)
Q.32Medium
The reciprocity theorem states that in a linear bilateral network:
Answer: C
Reciprocity theorem: If a voltage source at port 1 produces current at port 2, then the same source at port 2 produces equal current at port 1. Applicable for bilateral linear networks.
Q.33Medium
In a circuit, the star-delta transformation is used to:
Answer: D
Star-delta transformation converts between two three-terminal network configurations, simplifying circuit analysis by eliminating nodes that cannot be solved directly.
Q.34Medium
In mesh analysis, if a circuit has dependent sources, the approach is:
Answer: B
Mesh analysis works with dependent sources by expressing the controlling variable in terms of mesh currents, then solving the resulting equations.
Q.35Medium
The Norton equivalent of a network is found by:
Answer: C
Norton equivalent: IN = Isc (short-circuit current) and RN = Rth (equivalent resistance). Norton and Thevenin equivalents are related: Vth = IN × RN
Q.36Medium
In a circuit with mutual inductance between two coils, the coupling coefficient k is defined as:
Answer: B
Coupling coefficient k = M/√(L₁L₂), where 0 ≤ k ≤ 1. k=1 indicates perfect coupling, k=0 means no coupling.
Q.37Medium
In a magnetically coupled circuit with two inductors L₁ and L₂ with mutual inductance M, if current increases in primary, the induced voltage in secondary opposes this change. This demonstrates:
Answer: C
Faraday's law describes EMF generation; Lenz's law describes the direction (opposition to change). Both apply to mutual inductance phenomena.
Q.38Medium
A network is said to be bilateral if:
Answer: B
Bilateral networks are linear networks where reciprocal relationships hold. Networks with ideal diodes are unilateral (non-bilateral).
Q.39Medium
For a two-port network, if Z-parameters are known, the relationship between input impedance and Z11 is:
Answer: C
Z11 is defined as input impedance with port 2 open-circuited (I2=0). Therefore, Zin = Z11 only under this condition.
Q.40Medium
In a circuit with a dependent voltage source controlled by current, the controlling current flows through:
Answer: C
A CCVS (Current-Controlled Voltage Source) depends on current through any element in the control branch, measured in the specified reference direction.
