BME2301 Circuit Theory Quiz - Capacitors

BME2301 - Circuit Theory

• Course instructor: Dr. Görkem SERBES (office C317)
• Instructor email: [email protected]
• Instructor website: https://avesis.yildiz.edu.tr/gserbes/
• Lab assistant: Fatih Ekrem ONAT, email: [email protected]

Energy Storage Devices: Capacitors and Inductors

• Capacitors: Consist of two conductive plates separated by an insulator (dielectric). Commonly depicted as parallel metal plates separated by a distance (d).
• Formula for capacitance (C): C = εA/d, where ε is the permittivity (ε₀ * εᵣ, εᵣ is the relative permittivity), A is the plate area.
• Capacitors store energy in the electric field between the plates.
• Charging a capacitor involves applying a current for a finite time to its terminals.
• Discharging a capacitor involves the capacitor providing current to a circuit for a finite time.
  • Charging formula: v(t) = (1/C)∫₀ᵗ i(τ) dτ + v(0)
  • Discharging formula: v(t) = v(0) e^(-t/RC), where R is the resistance
• Capacitance increases with:
  • Increasing surface area of the plates
  • Decreasing spacing between the plates
  • Increasing the relative dielectric constant of the insulator between the plates.
• Various capacitor types exist (fixed, electrolytic, variable, MEMS, etc.).
  • Fixed capacitors (nonpolarized) can be connected in various ways.
  • Electrolytic capacitors have polarity constraints (e.g. negative terminal must be at a lower voltage) - these are often polarized, meaning they only accept a current in one direction
• Inductors: Typically coils of conducting wire, sometimes wrapped around a solid core (referred to as 'air core' if no core is used).
  • Inductors store energy in magnetic fields generated by current flow.
  • Inductors resist changes in current.
  • Formula for voltage(VL) across an inductor: VL = L di/dt - where L is the inductance
  • Formula for current (iL) through an inductor: iL = (1/L) ∫₀ᵗ vL dτ + i(0)
• Different types of inductors (e.g. reactors, chokes, coils, and solenoids) serve various functions.
  • Reactors and chokes are used in power grids and RF circuits.
• Inductors oppose sudden changes in current.
• Both capacitors and inductors are energy storage devices that control current and voltage.

Reading Capacitor Codes

• Codes typically consist of numerical digits followed by a letter and/or a decimal point.
• The first two digits or first two digits plus a letter usually represent the numerical value of capacitance.
• If the code includes letters other than R (e.g. p, n, or u), the letter indicates the units - these are often picofarads (pF), nanofarads (nF), and microfarads (µF)
• Voltage codes (often a letter) specify the maximum working voltage for DC capacitors.
• The value of the capacitance must be interpreted according to the unit notation following the third digit
• The third digit specifies multiplier. (e.g., zeros are added for digits 0 to 6).
• The third digit can also specify multiplier by a decimal value (8 means 0.01, 9 means 0.1).
• Tolerance codes (often a letter immediately following the numerical value) provide the amount of variation likely to be found in the capacitor's properties measured.

Equivalent Capacitance

• Capacitors in Parallel: Ceq = C₁ + C₂ + C₃ + ... + Cₚ
• Capacitors in Series: Ceq = (1/(C₁⁻¹) + (1/C₂⁻¹) + (1/C₃⁻¹) + ... (1/Cₛ⁻¹))
• The equivalent capacitance for a combination of capacitors in parallel or series can be calculated using the relevant equation.

Equivalent Inductance

• Inductors in Series: L⁻¹eq= (1/L₁ +1/L₂ +1/L₃+...1/Lₛ)
• Inductors in Parallel: L⁻¹eq = (L₁⁻¹ + L₂⁻¹ + L₃⁻¹ +...+ Lₚ⁻¹)

Properties of Capacitors

• At steady state, a capacitor in a DC circuit acts as an open circuit.
• A capacitor's voltage must be continuous.
• A real capacitor dissipates energy due to leakage through the insulating material
• Equivalent parallel capacitance is calculated by summing all parallel capacitance values.
• Equivalent series capacitance is calculated by summing the inverses of parallel capacitance values.

Properties of Inductors

• At steady state, an inductor in a DC circuit acts as a short circuit.
• An inductor's current must be continuous.
• A real inductor dissipates energy due to resistance in the wire and capacitive coupling between turns of the wire
• Equivalent parallel inductance is calculated as the inverse of the sum of inverses.
• Equivalent series inductance is calculated by summing all series inductance values

Example Problems

• Various example problems concerning capacitor and inductor behavior are covered in the presentation.

Test your knowledge on capacitors and inductors covered in BME2301. This quiz includes topics such as capacitance formulas and the processes of charging and discharging capacitors. Prepare to apply your understanding of energy storage devices in electrical engineering.