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Questions and Answers
What is the formula for capacitance defined in terms of the dimensions and materials of a capacitor?
What is the formula for capacitance defined in terms of the dimensions and materials of a capacitor?
Which factor increases capacitance according to the content?
Which factor increases capacitance according to the content?
What type of capacitor is described as nonpolarized and can connect with either terminal to the high voltage side of a circuit?
What type of capacitor is described as nonpolarized and can connect with either terminal to the high voltage side of a circuit?
What is the relationship between charge, voltage, and capacitance for a capacitor?
What is the relationship between charge, voltage, and capacitance for a capacitor?
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How is equivalent capacitance determined when multiple capacitors are connected in series?
How is equivalent capacitance determined when multiple capacitors are connected in series?
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What is the primary role of a capacitor in an electrical circuit?
What is the primary role of a capacitor in an electrical circuit?
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Which type of capacitor is primarily used in high voltage and high current applications?
Which type of capacitor is primarily used in high voltage and high current applications?
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What happens when a DC voltage is applied to an ideal capacitor?
What happens when a DC voltage is applied to an ideal capacitor?
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Which statement accurately describes how real capacitors differ from ideal capacitors?
Which statement accurately describes how real capacitors differ from ideal capacitors?
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How is the voltage across a capacitor expected to change in an ideal scenario?
How is the voltage across a capacitor expected to change in an ideal scenario?
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What happens when a DC voltage or current is applied to an ideal capacitor for at least 5 time constants?
What happens when a DC voltage or current is applied to an ideal capacitor for at least 5 time constants?
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Which of the following statements about the current flowing across a capacitor is true?
Which of the following statements about the current flowing across a capacitor is true?
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What does the equation for equivalent capacitance of capacitors in parallel represent?
What does the equation for equivalent capacitance of capacitors in parallel represent?
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Which term is often used to denote an inductor designed to block specific frequencies in RF circuits?
Which term is often used to denote an inductor designed to block specific frequencies in RF circuits?
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What occurs when the current through an inductor decreases?
What occurs when the current through an inductor decreases?
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What is the primary factor limiting additional charge storage in a capacitor as more charge is added?
What is the primary factor limiting additional charge storage in a capacitor as more charge is added?
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How does the voltage across a capacitor change as more charge is added?
How does the voltage across a capacitor change as more charge is added?
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What occurs when charge is being removed from a capacitor?
What occurs when charge is being removed from a capacitor?
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What happens to the force needed to drive charge off the plates of a capacitor as charge decreases?
What happens to the force needed to drive charge off the plates of a capacitor as charge decreases?
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What is indicated by the equation Q = CV in relation to a capacitor?
What is indicated by the equation Q = CV in relation to a capacitor?
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Study Notes
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
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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
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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.
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Description
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.
