AC Circuits — MHT-CET Physics

Formulas (2)

• Reading a Sinusoid: Peak Times, Zeros and Phase · Instantaneous value
  $$i = I_0\sin(\omega t + \phi), \qquad \omega = 2\pi f$$
• Peak and R.M.S. Values · R.m.s. value
  $$I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \approx 0.707\,I_0$$

Watch out for (2)

• Forgetting the starting phase
  → Reading a Sinusoid: Peak Times, Zeros and Phase
• Using the peak where the r.m.s. is meant
  → Peak and R.M.S. Values

Formulas (3)

• How Reactance Depends on Frequency, L and C · Reactances
  $$X_L = \omega L, \qquad X_C = \frac{1}{\omega C}$$
• Current and Phase With a Single L or C · CIVIL
  $$\text{C: } I \text{ leads } V \text{ by } 90^\circ; \qquad \text{L: } V \text{ leads } I \text{ by } 90^\circ$$
• A Bulb in Series With a Coil or a Capacitor · Current falls as reactance rises
  $$I = \frac{V}{\sqrt{R^2 + X^2}}$$

Watch out for (3)

• Treating X_C like X_L
  → How Reactance Depends on Frequency, L and C
• Swapping lead and lag
  → Current and Phase With a Single L or C
• Reversing the capacitor's rule
  → A Bulb in Series With a Coil or a Capacitor

Formulas (3)

• Impedance and Current · Impedance
  $$Z = \sqrt{R^2 + (X_L - X_C)^2}$$
• The Phase Angle · Phase angle
  $$\tan\phi = \frac{X_L - X_C}{R}$$
• Voltages Add as Phasors · Series voltages
  $$V = \sqrt{V_R^2 + (V_L - V_C)^2}$$

Watch out for (3)

• Adding R and X directly
  → Impedance and Current
• Inverting the tangent
  → The Phase Angle
• Adding the voltages as numbers
  → Voltages Add as Phasors

Formulas (3)

• The Resonant Frequency · Resonant frequency
  $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
• What Happens at Resonance · At resonance
  $$X_L = X_C, \quad Z = R, \quad \phi = 0$$
• Voltages Across L and C at Resonance, and the Quality Factor · Quality factor
  $$Q = \frac{V_L}{V_R} = \frac{1}{R}\sqrt{\frac{L}{C}}$$

Watch out for (3)

• 'Increased by 3C' is 4C
  → The Resonant Frequency
• Impedance zero at resonance
  → What Happens at Resonance
• Capping V_L at the supply voltage
  → Voltages Across L and C at Resonance, and the Quality Factor

Formulas (3)

• Average Power · Average power
  $$P = V_{\text{rms}}I_{\text{rms}}\cos\phi = I_{\text{rms}}^2R$$
• Power Factor · Power factor
  $$\cos\phi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + (X_L - X_C)^2}}$$
• Wattless Current · Purely reactive circuit
  $$\phi = 90^\circ \;\Rightarrow\; P = V_{\text{rms}}I_{\text{rms}}\cos 90^\circ = 0$$

Watch out for (3)

• Using peak values without the ½
  → Average Power
• Doubling the frequency of an RC circuit
  → Power Factor
• Current means power
  → Wattless Current

Formulas (3)

• LC Oscillations · LC circuit
  $$T = 2\pi\sqrt{LC}, \qquad I_0 = V\sqrt{\frac{C}{L}}$$
• The Transformer · Transformer
  $$\frac{V_s}{V_p} = \frac{N_s}{N_p}, \qquad \eta = \frac{V_sI_s}{V_pI_p}$$
• The AC Generator · Generator e.m.f.
  $$e_0 = NAB\omega, \qquad \bar P = \frac{(NAB\omega)^2}{2R}$$

Watch out for (3)

• Taking the full period for 'current greatest'
  → LC Oscillations
• Applying the efficiency to the primary current
  → The Transformer
• Squaring only part of e₀
  → The AC Generator