Cylindrical and Spherical Capacitors
- Capacitors are devices that store electric charge and energy.
- Cylindrical Capacitors: Consist of two concentric cylindrical conductors.
- Spherical Capacitors: Consist of two concentric spherical conductors.
- The capacitance of a cylindrical or spherical capacitor depends on the geometry and dielectric properties.
- Capacitance (C) is measured in Farads (F).
Series Combination of Capacitors
- When capacitors are connected in series, the total capacitance (Ct) decreases.
- The inverse of the total capacitance (1/Ct) is equal to the sum of the inverses of individual capacitances (1/C1 + 1/C2 + 1/C3 + …).
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- 1/Ct = 1/2 + 1/3 + 1/4 = 13/12
- Ct = 12/13 μF
Parallel Combination of Capacitors
- When capacitors are connected in parallel, the total capacitance (Ct) increases.
- The total capacitance (Ct) is equal to the sum of individual capacitances (C1 + C2 + C3 + …).
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- Ct = 2 + 3 + 4 = 9 μF
Energy Stored in a Capacitor
- The energy stored in a capacitor is given by the equation:
- E = 0.5 * C * V^2
- E: Energy stored (in joules)
- C: Capacitance (in farads)
- V: Voltage across the capacitor (in volts)
- E = 0.5 * C * V^2
- Example: C = 5 μF, V = 10 V
- E = 0.5 * 5 * (10^2) = 250 μJ
Introduction to Capacitors
- Capacitors are passive electronic components used to store and release electrical energy.
- They consist of two conductive plates separated by a dielectric material.
- Capacitors are characterized by their capacitance value, voltage rating, and tolerance.
- They can store electric charge, resist changes in voltage, and are used in various applications, such as filters and timing circuits.
- Capacitors can be polarized or non-polarized, depending on their construction.
Capacitance of a Capacitor
- Capacitance (C) is the ability of a capacitor to store electrical charge.
- It is defined as the ratio of the stored charge (Q) to the applied voltage (V): C = Q/V.
- Capacitance is measured in Farads (F).
- The capacitance depends on the geometry of the capacitor, including the area of the plates, the distance between the plates, and the dielectric material used.
Dielectric Material
- The dielectric material is an insulating material placed between the conductive plates of a capacitor.
- It increases the capacitance of the capacitor by reducing the electric field and increasing the charge storage.
- Common dielectric materials include air, paper, ceramic, mica, and various types of plastic.
- The dielectric constant (k) of a material determines its ability to store charge. Higher k means higher capacitance.
Capacitance Calculation for Cylindrical Capacitor
- For a cylindrical capacitor with inner radius (r1), outer radius (r2), and length (l):
- The capacitance is given by: C = (2πε0εr * l) / ln(r2/r1)
- ε0: Vacuum permittivity (8.85 x 10^-12 F/m)
- εr: Relative permittivity (dielectric constant) of the material between the cylinders
- The capacitance is given by: C = (2πε0εr * l) / ln(r2/r1)
Capacitance Calculation for Spherical Capacitor
- For a spherical capacitor with inner radius (r1) and outer radius (r2):
- The capacitance is given by: C = (4πε0εr * r1 * r2) / (r2 - r1)
- ε0: Vacuum permittivity (8.85 x 10^-12 F/m)
- εr: Relative permittivity (dielectric constant) of the material between the spheres
- The capacitance is given by: C = (4πε0εr * r1 * r2) / (r2 - r1)
Energy Stored in a Capacitor (continued)
- The energy stored in a capacitor can also be expressed as:
- E = 0.5 * Q * V, where Q is the charge stored and V is the voltage across the capacitor.
- The energy is directly proportional to both the square of the charge and the voltage.
- Example: Q = 50 μC, V = 100 V
- E = 0.5 * (50 x 10^-6) * (100^2) = 0.25 Joules
Slide 11: Cylindrical Capacitors
- Cylindrical capacitors consist of two concentric cylindrical conductors.
- They are commonly used in applications where cylindrical symmetry is desired.
- The capacitance of a cylindrical capacitor depends on the geometry and dielectric properties.
- The capacitance can be calculated using the formula: C = (2πε0εr * l) / ln(r2/r1), where l is the length between the cylinders.
- Dielectric material between the cylinders affects the capacitance.
Slide 12: Spherical Capacitors
- Spherical capacitors consist of two concentric spherical conductors.
- They are commonly used in applications where spherical symmetry is desired.
- The capacitance of a spherical capacitor depends on the geometry and dielectric properties.
- The capacitance can be calculated using the formula: C = (4πε0εr * r1 * r2) / (r2 - r1), where r1 and r2 are the radii of the spheres.
- Dielectric material between the spheres affects the capacitance.
Slide 13: Series Combination of Capacitors
- When capacitors are connected in series, the total capacitance decreases.
- The inverse of the total capacitance is equal to the sum of the inverses of individual capacitances.
- Mathematically, 1/Ct = 1/C1 + 1/C2 + 1/C3 + …
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- 1/Ct = 1/2 + 1/3 + 1/4 = 13/12
- Ct = 12/13 μF
Slide 14: Parallel Combination of Capacitors
- When capacitors are connected in parallel, the total capacitance increases.
- The total capacitance is equal to the sum of individual capacitances.
- Mathematically, Ct = C1 + C2 + C3 + …
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- Ct = 2 + 3 + 4 = 9 μF
Slide 15: Energy Stored in a Capacitor
- The energy stored in a capacitor can be calculated using the formula: E = 0.5 * C * V^2.
- The energy is directly proportional to both the square of the capacitance (C) and the voltage (V).
- The unit of energy stored is joules (J).
- Example: C = 5 μF, V = 10 V
- E = 0.5 * 5 * (10^2) = 250 μJ
Slide 16: Introduction to Capacitors
- Capacitors are passive electronic components used to store and release electrical energy.
- They consist of two conductive plates separated by a dielectric material.
- Capacitors can store electric charge, resist changes in voltage, and have various applications.
- They are commonly used in circuits for filtering, timing, energy storage, and power factor correction.
- Capacitors come in different types and sizes, suitable for different applications.
Slide 17: Capacitance of a Capacitor
- Capacitance (C) is a measure of a capacitor’s ability to store electrical charge.
- It is defined as the ratio of the stored charge (Q) to the applied voltage (V): C = Q/V.
- The unit of capacitance is the Farad (F).
- Capacitance depends on the geometry of the capacitor, dielectric material, and distance between plates.
- It can range from picofarads (pF) to farads (F) depending on the capacitor type.
Slide 18: Dielectric Material
- Dielectric material is an insulating substance used between the conductive plates of a capacitor.
- It increases the capacitance by reducing the electric field and enhancing charge storage.
- Dielectrics can be solid, liquid, or gas, with different dielectric constants (relative permittivity).
- Common dielectric materials include air, paper, ceramic, mica, and various types of plastic.
- Dielectric constant (k) determines the capacitance enhancement; higher k means higher capacitance.
Slide 19: Capacitance Calculation for Cylindrical Capacitor
- The capacitance (C) of a cylindrical capacitor with inner radius (r1), outer radius (r2), and length (l) can be calculated using the formula:
- C = (2πε0εr * l) / ln(r2/r1)
- Here, ε0 is the vacuum permittivity (8.85 x 10^-12 F/m) and εr is the relative permittivity (dielectric constant).
Slide 20: Capacitance Calculation for Spherical Capacitor
- The capacitance (C) of a spherical capacitor with inner radius (r1) and outer radius (r2) can be calculated using the formula:
- C = (4πε0εr * r1 * r2) / (r2 - r1)
- Here, ε0 is the vacuum permittivity (8.85 x 10^-12 F/m) and εr is the relative permittivity (dielectric constant).
Slide 21: Uses of Capacitors
- Capacitors are used in various electronic and electrical circuits.
- Some common applications of capacitors include:
- Filtering and smoothing out voltage fluctuations in power supplies.
- Storing energy for flash cameras and strobe lights.
- Timing circuits in electronic devices.
- Coupling and decoupling signals between different stages of amplifiers.
- Power factor correction in electrical systems.
- Motor start and run capacitors in AC motors.
- Energy storage in renewable energy systems.
Slide 22: Capacitors in Filters
- Capacitors are commonly used in electronic filters to pass or block certain frequencies.
- They can be used in low-pass, high-pass, band-pass, and band-stop filters.
- In a low-pass filter, high-frequency signals are attenuated, and low-frequency signals are allowed to pass.
- In a high-pass filter, low-frequency signals are attenuated, and high-frequency signals are allowed to pass.
- Band-pass filters allow a specific range of frequencies to pass, while blocking others.
- Band-stop filters (also called notch filters) block a specific range of frequencies.
Slide 23: Capacitors in Timing Circuits
- Capacitors are used in timing circuits to control the duration of signals or delays.
- They can be used in RC (resistor-capacitor) and LC (inductor-capacitor) timing circuits.
- In an RC timing circuit, the charging and discharging of a capacitor through a resistor determines the timing.
- Timing circuits are commonly used in applications such as delay switches, oscillators, and pulse generators.
- The time constant (R*C) of a timing circuit determines the timing behavior.
Slide 24: Capacitors in AC Applications
- Capacitors play important roles in AC circuits.
- They are used for power factor correction, where the leading or lagging power factor is adjusted.
- Capacitors can also be used to reduce voltage dips and transient disturbances in electrical systems.
- They are employed in AC motor start and run circuits to control the motor’s starting and running behavior.
- Motor run capacitors are continuously connected to the motor, while start capacitors are temporarily connected during startup.
Slide 25: Capacitors and Energy Storage
- Capacitors can store electrical energy, and their ability to quickly charge and discharge makes them suitable for energy storage applications.
- They are used in flash cameras, strobe lights, and other devices that require bursts of energy.
- Capacitors can also be part of energy storage systems, such as supercapacitors and electric vehicle batteries.
- Energy storage systems based on capacitors can provide quick bursts of power and contribute to load balancing in power grids.
Slide 26: Equivalent Capacitance in Series
- Capacitors connected in series have a reduced equivalent capacitance.
- To find the equivalent capacitance (Ct), use the formula: 1/Ct = 1/C1 + 1/C2 + 1/C3 + …
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- 1/Ct = 1/2 + 1/3 + 1/4 = 13/12
- Ct = 12/13 μF
Slide 27: Equivalent Capacitance in Parallel
- Capacitors connected in parallel have an increased equivalent capacitance.
- To find the equivalent capacitance (Ct), simply add up the individual capacitances: Ct = C1 + C2 + C3 + …
- Example: C1 = 2 μF, C2 = 3 μF, C3 = 4 μF
- Ct = 2 + 3 + 4 = 9 μF
Slide 28: Capacitors and Voltage
- Capacitors store electrical energy in the form of electric field potential energy.
- The voltage (V) across a capacitor is directly proportional to the stored charge (Q) and inversely proportional to the capacitance (C): V = Q/C.
- When the voltage across a capacitor changes, the charge stored in the capacitor changes accordingly.
- Capacitors resist changes in voltage, allowing them to stabilize voltage levels in circuits.
Slide 29: Energy Stored in a Capacitor
- The energy (E) stored in a capacitor can be calculated using the formula: E = 0.5 * C * V^2.
- The energy is directly proportional to both the capacitance (C) and the square of the voltage (V).
- Example: C = 5 μF, V = 10 V
- E = 0.5 * 5 * (10^2) = 250 μJ
Slide 30: Summary
- Capacitors are essential electronic components used for energy storage, filtering, timing, and power factor correction.
- Their capacitance depends on geometry, dielectric properties, and distance between plates.
- Capacitors can be connected in series or parallel to modify their equivalent capacitance.
- The stored energy in a capacitor is given by 0.5 * C * V^2 formula.
- Understanding capacitors and their applications is crucial for various fields of electrical engineering and electronics.
Cylindrical and Spherical Capacitors Capacitors are devices that store electric charge and energy. Cylindrical Capacitors: Consist of two concentric cylindrical conductors. Spherical Capacitors: Consist of two concentric spherical conductors. The capacitance of a cylindrical or spherical capacitor depends on the geometry and dielectric properties. Capacitance (C) is measured in Farads (F).