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Physics: Capacitors and Electric Quantities

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  • Letter and unit for electric charge
    Electric charge is represented by \(q\text{ or }Q\) and measured in coulombs (C).
  • Letter and unit for electric potential
    Electric potential is represented by \(V\) and measured in volts (V).
  • Letter and unit for electric potential energy
    Electric potential energy is represented by \(U\) and measured in joules (J).
  • Letter and unit for energy density
    Energy density is represented by \(u\) and measured in joules per cubic meter (J/m³).
  • Letter and unit for capacitance
    Capacitance is represented by \(C\) and measured in farads (F).
  • Definition equation for capacitance
    Capacitance is defined by the equation \(Q=VC\), relating charge, voltage, and capacitance.
  • Equivalent capacitance for capacitors in series
    For capacitors in series: \(\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\dots\).
  • Charge on capacitors in series
    Charge is the same on all capacitors in series: \(Q_{tot}=Q_1=Q_2=Q_3=\dots\).
  • Voltage across capacitors in series
    Total voltage is the sum of voltages: \(V_{tot}=V_1+V_2+V_3+\dots\).
  • Equivalent capacitance for capacitors in parallel
    For capacitors in parallel: \(C_{eq}=C_1+C_2+C_3+\dots\).
  • Charge on capacitors in parallel
    Total charge is the sum of charges: \(Q_{tot}=Q_1+Q_2+Q_3+\dots\).
  • Voltage across capacitors in parallel
    Voltage is the same across all capacitors in parallel: \(V_{tot}=V_1=V_2=V_3=\dots\).
  • Capacitance of a parallel-plate capacitor
    Capacitance is given by \(C=\kappa \varepsilon_0 \frac{A}{d}\), where κ is dielectric constant, ε₀ permittivity, A area, and d plate separation.
  • Electric field inside a parallel-plate capacitor
    Electric field is \(E=\frac{\Delta V}{d}\), voltage difference divided by plate separation.
  • Meaning of dielectric strength
    Dielectric strength is the maximum electric field before breakdown occurs, causing current flow and capacitor discharge.
  • Dielectric strength of air
    The dielectric strength of air is \(E_{Max,air}=3.0 \times 10^{6} \text{ V/m}\).
  • Formulas for electric potential energy stored in a capacitor
    Energy stored can be calculated by \(U_C=\frac{1}{2}CV^2\), \(U_C=\frac{Q^2}{2C}\), or \(U_C=\frac{1}{2}QV\).
  • General definition of energy density
    Energy density is defined as \(u=\frac{U_C}{\text{Vol}}\), energy per unit volume.
  • Energy density for an electric field
    Energy density in an electric field is \(u=\frac{1}{2}\kappa \varepsilon_0 E^2\).