Basic Electrical Circuits and AC Fundamentals for SSC JE Electrical: RMS, Impedance, Power Factor, Resonance and Three-Phase
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Basic electrical engineering and AC fundamentals form the base of every SSC JE Electrical paper. Questions come from the laws of circuits, the RMS value, the impedance, the power factor, the resonance and the three-phase formulas. This guide on basic electrical circuits and AC fundamentals for SSC JE covers all of them in tables, with solved examples, practice questions and FAQs.
Basic Laws and Quantities
| Law or Quantity | Statement or Formula |
|---|---|
| Ohm’s law | V = I R (at constant temperature) |
| Kirchhoff’s current law (KCL) | The algebraic sum of the currents at a node is zero |
| Kirchhoff’s voltage law (KVL) | The algebraic sum of the voltages in a closed loop is zero |
| Resistance of a conductor | R = ρ L / A |
| Resistors in series / parallel | R = R1 + R2 / 1/R = 1/R1 + 1/R2 |
| Power | P = VI = I²R = V²/R |
| Energy | E = P t; 1 kWh = 3.6 × 10⁶ J |
| Energy stored in a capacitor | ½ C V² |
| Energy stored in an inductor | ½ L I² |
| Time constant | τ = RC (RC circuit) and τ = L/R (RL circuit) |
AC Waveform Terms
| Term | Value for a Sine Wave |
|---|---|
| Average value | 2Vm/π = 0.637 Vm |
| RMS (effective) value | Vm/√2 = 0.707 Vm |
| Form factor | RMS / average = 1.11 |
| Peak (crest) factor | Peak / RMS = 1.414 |
| Frequency | f = 1/T; in India 50 Hz (T = 20 ms) |
| Angular frequency | ω = 2πf |
The RMS value of an AC is the value of the DC that produces the same heating effect; the ordinary AC meters read RMS values. A 230 V supply has a peak value of 230 × 1.414 = 325 V.
Reactance, Impedance and Phase
| Element | Reactance | Phase of Current w.r.t. Voltage |
|---|---|---|
| Resistor (R) | R | In phase |
| Inductor (L) | XL = 2πfL | Lags the voltage by 90° |
| Capacitor (C) | XC = 1/(2πfC) | Leads the voltage by 90° |
- Series RLC circuit: impedance Z = √(R² + (XL − XC)²); the phase angle φ = tan⁻¹((XL − XC)/R).
- The circuit is inductive if XL > XC (current lags), capacitive if XC > XL (current leads).
- Remember CIVIL: in a capacitor (C) the current (I) leads the voltage (V); in an inductor (L) the voltage leads the current.
- Admittance Y = 1/Z; conductance G = 1/R; susceptance B = 1/X.
Power in AC Circuits
| Power | Formula | Unit |
|---|---|---|
| Real (active) power | P = V I cosφ | Watt (W) |
| Reactive power | Q = V I sinφ | Volt-ampere reactive (VAR) |
| Apparent power | S = V I | Volt-ampere (VA) |
| Power factor | cosφ = P/S = R/Z | Dimensionless (0 to 1) |
The power factor is lagging for an inductive load and leading for a capacitive load; a low power factor increases the current, the losses and the voltage drop. It is improved by connecting capacitors in parallel with the load (or a synchronous condenser).
Resonance
| Feature | Series Resonance | Parallel Resonance |
|---|---|---|
| Condition | XL = XC | Reactive currents of L and C are equal |
| Resonant frequency | f0 = 1/(2π√LC) | Same formula (ideal case) |
| Impedance | Minimum (= R) | Maximum |
| Current | Maximum | Minimum |
| Power factor | Unity | Unity |
| Quality factor | Q = ω0L/R = 1/R √(L/C); voltage magnification | Q = R√(C/L); current magnification |
| Name | Acceptor circuit | Rejector circuit |
Three-Phase Systems
| Connection | Line and Phase Voltage | Line and Phase Current |
|---|---|---|
| Star (Y) | VL = √3 Vph | IL = Iph |
| Delta (Δ) | VL = Vph | IL = √3 Iph |
- Total power in a balanced three-phase system: P = √3 VL IL cosφ (for both star and delta).
- The phase difference between the three voltages is 120°; the phase sequence is RYB.
- The two-wattmeter method measures the three-phase power: W1 + W2 = P; the power factor is cosφ with tanφ = √3 (W1 − W2)/(W1 + W2); at unity pf both read the same; at 0.5 pf one wattmeter reads zero.
- Star–delta conversion: Rstar = Rdelta/3.
- The neutral carries no current in a balanced star load.
Solved Examples
Example 1. Find the peak value of a 230 V RMS supply.
230 × 1.414 = 325.3 V.
Example 2. A series circuit has R = 30 Ω and XL = 40 Ω. Find the impedance and the power factor.
Z = √(900 + 1600) = 50 Ω; cosφ = 30/50 = 0.6 lagging.
Example 3. A three-phase load takes 10 A at 400 V line voltage and a power factor of 0.8. Find the power.
P = √3 × 400 × 10 × 0.8 = 5,542 W.
Example 4. Find the resonant frequency for L = 1 mH and C = 10 µF.
f0 = 1/(2π√(10⁻³ × 10⁻⁵)) = 1/(2π × 10⁻⁴) = 1,591 Hz.
Quick Tips
- Memorise 0.707, 0.637, 1.11 and 1.414 for the sine wave.
- Remember CIVIL for the phase relations.
- Remember that the three-phase power formula is the same for star and delta.
- Remember the minimum impedance at series resonance.
Quick Revision Points
- RMS = 0.707 Vm; average = 0.637 Vm.
- XL = 2πfL; XC = 1/2πfC.
- Power factor = cosφ = R/Z.
- Series resonance: Z is minimum and I is maximum.
- Star: VL = √3 Vph; delta: IL = √3 Iph.
Practice Questions With Answers
- What is the RMS value of a sine wave of peak 100 V?
Answer: 70.7 V - What is the form factor of a sine wave?
Answer: 1.11 - What is the power factor of a pure inductor?
Answer: Zero (lagging) - What is the impedance at series resonance?
Answer: Minimum, equal to R - What is the resonant frequency formula?
Answer: 1/(2π√LC) - What is the relation between line and phase voltage in a star connection?
Answer: VL = √3 Vph - What is the unit of reactive power?
Answer: VAR - In a capacitor, does the current lead or lag the voltage?
Answer: Lead by 90° - How is the power factor improved?
Answer: By connecting a capacitor in parallel with the load - What is the unit of the apparent power?
Answer: VA
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Electrical Engineering notes page and the next topic DC Machines: Generators and Motors.
Frequently Asked Questions
What is Ohm’s law?
The current through a conductor is proportional to the voltage across it: V = IR.
What is the RMS value?
The effective value of an AC that gives the same heating effect as a DC of that value.
What is impedance?
The total opposition to an AC in a circuit, made up of resistance and reactance.
What is the power factor?
The ratio of the real power to the apparent power, cosφ.
What is resonance?
The condition in which the inductive and capacitive reactances are equal.
What is a quality factor?
A measure of the sharpness of resonance, Q = ωL/R.
What is the line voltage in a star connection?
√3 times the phase voltage.
What is the two-wattmeter method?
A method of measuring the three-phase power with two wattmeters.
What is a reactive power?
The power that oscillates between the source and the reactive elements; Q = VI sinφ.
Is this topic asked in SSC JE?
Yes. AC fundamentals are asked in every SSC JE Electrical paper.
What is the frequency of the Indian power supply?
50 Hz.
What does KCL state?
The sum of currents entering a node equals the sum leaving it.
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DC Machines for SSC JE Electrical: DC Generators and Motors, EMF Equation, Types, Speed Control, Starters and Losses
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.