This chapter explores alternating current, a common form of electric power. It highlights its importance in daily life, especially in powering devices and its advantages over direct current.
ALTERNATING CURRENT – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the ALTERNATING CURRENT chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
v(t) = v_m sin(ωt)
v(t) is the instantaneous voltage (volts), v_m is the peak voltage (volts), ω is the angular frequency (radians/second). Describes how voltage varies in an AC circuit.
i(t) = i_m sin(ωt + φ)
i(t) is the instantaneous current (amperes), i_m is the peak current (amperes), and φ is the phase angle (radians). Specifies current variation in AC circuits.
i_m = v_m / X_L
X_L is the inductive reactance (ohms). Relates peak current to peak voltage in a purely inductive circuit.
X_L = ωL
X_L is the inductive reactance (ohms) where L is inductance (henries) and ω = 2πf (radians/second). Indicates how inductance affects circuit behavior.
X_C = 1/(ωC)
X_C is the capacitive reactance (ohms) where C is capacitance (farads). Details the current-limiting effect of capacitors in an AC circuit.
Z = √(R² + (X_L - X_C)²)
Z is the impedance (ohms) in an RLC circuit, combining resistance (R) and reactance (X_L, X_C). Determines overall opposition to AC current.
P = VI cos φ
P is the average power (watts), V is the rms voltage (volts), I is the rms current (amperes). Accounts for power factoring in phase difference in AC circuits.
I_rms = i_m / √2
I_rms is the root mean square current (amperes), i_m is the peak current (amperes). Provides effective current measurement for AC circuits.
V_rms = v_m / √2
V_rms is the root mean square voltage (volts), v_m is the peak voltage (volts). Defines effective voltage for AC applications.
ω₀ = 1/√(LC)
ω₀ is the resonant frequency (radians/second). Indicates frequency at which LCR circuit resonance occurs.
Equations
p = (1/2)i²R
p is instantaneous power (watts). Indicates power loss due to Joule heating in a resistor in AC circuits.
φ = tan⁻¹((X_L - X_C) / R)
φ is the phase difference (radians) between voltage and current in an LCR circuit. Shows relationship between reactance and resistance.
P_avg = I_rms²R
P_avg is the average power (watts) in a resistive AC circuit. Shows power losses in terms of rms current.
V = I_rms * Z
Relates voltage (voltage drop) across an impedance in an AC circuit to its rms current and impedance.
maximum power occurs at resonance when X_L = X_C
Demonstrates that at resonant frequency, the inductive and capacitive reactances balance, maximizing the circuit current.
P = V² / Z
P is the average power (watts), V is the rms voltage (volts), Z is the impedance (ohms). Gives another form to calculate power.
E = N_dΦ/dt
E is induced EMF (volts) based on changing magnetic flux (Φ, webers) linked to coil with N (turns). Fundamental principle of transformers.
V_s / V_p = N_s / N_p
Gives the relation between primary and secondary voltages in a transformer based on number of turns in coils.
I_s / I_p = N_p / N_s
Shows inversely proportional relationship between primary and secondary currents based on number of turns in a transformer.
Z = √(R² + (X_L - X_C)²)
Derives total opposition (impedance) in RLC circuits considering resistive (R) and reactive (X_L, X_C) components.
This chapter explains electrostatic potential and capacitance, providing essential concepts necessary for understanding electric fields and energy storage in capacitors.
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Start chapterThis chapter discusses the relationship between moving charges and magnetic fields. It is crucial for understanding how electric currents generate magnetic fields and the effects of these fields on charged particles.
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