BEE Circuit Analysis 2 — Questions and Answers
Question 1: Kirchhoff's Current Law (KCL) states that:
- Voltage around a loop sums to zero
- Current entering a node equals current leaving (Correct answer)
- Power equals voltage times current
- Resistance is constant in all circuits
Correct answer: Current entering a node equals current leaving
KCL: The algebraic sum of currents at any node is zero (current in = current out).
KCL is based on conservation of charge. At any junction (node) in a circuit, the total current flowing in must equal the total current flowing out. Mathematically: ΣI_in = ΣI_out, or equivalently, ΣI = 0 at any node.
Question 2: Two 10Ω resistors connected in parallel have a combined resistance of:
- 20Ω
- 10Ω
- 5Ω (Correct answer)
- 2.5Ω
Correct answer: 5Ω
Parallel: 1/R_total = 1/10 + 1/10 = 2/10, so R_total = 5Ω.
For parallel resistors: 1/R_total = 1/R1 + 1/R2 = 1/10 + 1/10 = 2/10. Therefore R_total = 10/2 = 5Ω. Shortcut for equal resistors: R_total = R/n = 10/2 = 5Ω.
Question 3: The time constant (τ) of an RC circuit is:
- R + C
- R × C (Correct answer)
- R / C
- C / R
Correct answer: R × C
τ = RC (resistance × capacitance) in seconds.
The time constant τ = RC determines how quickly a capacitor charges or discharges. After one time constant, voltage reaches ~63.2% of final value. After 5τ, the capacitor is considered fully charged (~99.3%).
Question 4: In a series RLC circuit at resonance:
- Impedance is maximum
- Impedance is minimum (equals R only) (Correct answer)
- Current is minimum
- Voltage across L and C are zero
Correct answer: Impedance is minimum (equals R only)
At resonance, inductive and capacitive reactances cancel, leaving only R.
At resonant frequency (f₀ = 1/2π√LC), XL = XC so they cancel. Total impedance Z = R (minimum possible). Current is maximum. Voltage across L and C can exceed the source voltage but are equal and opposite.
Question 5: Thevenin's theorem allows a complex circuit to be represented as:
- A current source in parallel with resistance
- A voltage source in series with resistance (Correct answer)
- A single resistor
- An ideal transformer
Correct answer: A voltage source in series with resistance
Thevenin equivalent: open-circuit voltage source (Vth) in series with Thevenin resistance (Rth).
Thevenin's theorem states any linear two-terminal circuit can be replaced by an equivalent circuit of a voltage source (Vth = open-circuit voltage) in series with a resistance (Rth = resistance seen from terminals with sources killed).
Question 6: The unit of capacitance is:
- Henry
- Ohm
- Farad (Correct answer)
- Watt
Correct answer: Farad
Capacitance is measured in Farads (F). Common values are in µF, nF, or pF.
The Farad (F) is the SI unit of capacitance. One Farad = one coulomb per volt (C/V). Practical capacitors typically range from picofarads (pF) to millifarads (mF). Henrys are for inductance, Ohms for resistance, Watts for power.
BEE Circuit Analysis 2
Kirchhoff's Current Law (KCL) states that: