Alternating Current — Class 12 Physics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Physics chapter "Alternating Current" — 6 important questions with detailed answers for CBSE board exam preparation.
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TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Alternating Current" — 6 important questions with detailed answers for CBSE board exam…
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Key Questions Covered:
- Define AC current and voltage. Explain peak value, RMS value, and average value.
- Explain AC circuit with pure resistance. Draw phasor diagram and power equation.
- Explain AC circuit with pure inductance (L). Draw impedance and phasor diagram.
- Explain AC circuit with pure capacitance (C). Compare with inductance.
- Analyze AC series RLC circuit. Derive impedance and resonance condition.
- Explain transformer principle. Derive voltage and current transformation ratios.
Solutions Summary:
| Question | Status |
|---|---|
| Define AC current and voltage. Explain peak value, RMS va… | ✓ Solved |
| Explain AC circuit with pure resistance. Draw phasor diag… | ✓ Solved |
| Explain AC circuit with pure inductance (L). Draw impedan… | ✓ Solved |
| Explain AC circuit with pure capacitance (C). Compare wit… | ✓ Solved |
| Analyze AC series RLC circuit. Derive impedance and reson… | ✓ Solved |
| Explain transformer principle. Derive voltage and current… | ✓ Solved |
Showing 6 of 6 questions
Q1: Define AC current and voltage. Explain peak value, RMS value, and average value.
AC (Alternating Current): Electric current that reverses direction periodically with time.
I = I₀ sin(ωt + φ) or I = I₀ cos(ωt + φ)
where I₀ = peak (maximum) current
ω = angular frequency (rad/s)
t = time
φ = phase constant
AC Voltage: V = V₀ sin(ωt + φ)
where V₀ = peak voltage
Three Important Values:
1. Peak (Maximum) Value:
I_peak = I₀ (maximum value of current)
V_peak = V₀ (maximum value of voltage)
- Used in calculations of power dissipation in resistor
- Important for insulation desig...
Q2: Explain AC circuit with pure resistance. Draw phasor diagram and power equation.
AC Circuit with Pure Resistance (R):
Circuit: AC source connected to resistor R only (no L or C)
Voltage applied: V = V₀ sin(ωt)
Current through resistor (Ohm's law):
I = V/R = (V₀/R) sin(ωt) = I₀ sin(ωt)
where I₀ = V₀/R (peak current)
Key Observations:
1. Current and voltage in phase (φ = 0°)
2. No phase difference between I and V
3. Peak values related by: V₀ = I₀R
4. RMS values: V_rms = I_rms × R
Phasor Diagram (at t = 0):
- Draw V and I vectors both along same direction (horizontal)
- ...
Q3: Explain AC circuit with pure inductance (L). Draw impedance and phasor diagram.
AC Circuit with Pure Inductance (L):
Circuit: AC source connected to pure inductor only (no R or C)
Voltage applied: V = V₀ sin(ωt)
Induced emf in inductor:
ε = -L(dI/dt) = -V (opposes applied voltage)
From Faraday's law:
V = L(dI/dt)
V₀ sin(ωt) = L(dI/dt)
Integrating:
I = -(V₀/ωL) cos(ωt) = (V₀/ωL) sin(ωt - π/2)
I = I₀ sin(ωt - π/2)
where I₀ = V₀/ωL
Inductive Reactance:
X_L = ωL = 2πfL (Ohms, Ω)
where ω = 2πf (angular frequency)
f = frequency (Hz)
L = inductance (H)
Key Observations:
1...
Q4: Explain AC circuit with pure capacitance (C). Compare with inductance.
AC Circuit with Pure Capacitance (C):
Circuit: AC source connected to pure capacitor only (no R or L)
Voltage applied: V = V₀ sin(ωt)
Charge on capacitor:
Q = CV = CV₀ sin(ωt)
Current (rate of charge flow):
I = dQ/dt = CV₀ω cos(ωt)
I = CV₀ω sin(ωt + π/2)
I = I₀ sin(ωt + π/2)
where I₀ = CV₀ω = V₀/(1/ωC)
Capacitive Reactance:
X_C = 1/(ωC) = 1/(2πfC) (Ohms, Ω)
where ω = 2πf
C = capacitance (F)
Key Observations:
1. Current leads voltage by 90° (φ = +90°)
2. When V = maximum, I = 0
3. When V ...
Q5: Analyze AC series RLC circuit. Derive impedance and resonance condition.
AC Series RLC Circuit: Resistor, Inductor, Capacitor in series with AC source
Voltage distribution:
V = V_R + V_L + V_C = V₀ sin(ωt)
Voltage across elements:
V_R = IR (in phase with I)
V_L = IX_L (leads I by 90°)
V_C = IX_C (lags I by 90°)
Phasor Analysis:
- All currents same (series circuit)
- Net voltage from phasors
- V_L and V_C opposite direction (cancel partially)
Net reactance:
X = X_L - X_C = ωL - 1/(ωC)
Impedance (Z):
Z = √[R² + (X_L - X_C)²] = √[R² + (ωL - 1/ωC)²]
Alternatively:
...
Q6: Explain transformer principle. Derive voltage and current transformation ratios.
Transformer: Device that converts AC voltage and current using electromagnetic induction and mutual inductance.
Principle:
1. Primary coil (input): Connected to AC source
2. Iron core: Carries alternating magnetic field
3. Secondary coil (output): Magnetic field induces emf
4. Mutual inductance couples the coils
Theory (Ideal Transformer):
Primary coil:
- N₁ turns
- Voltage V₁ = V₁₀ sin(ωt)
- Current I₁
- Induced emf by changing flux: ε₁ = -N₁(dΦ/dt)
Secondary coil:
- N₂ turns
- Voltage V₂ (...
Showing 6 of 6 questions. Visit the full page for complete solutions.
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