Passive Circuit Components
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Passive circuit components include resistors, capacitors, and inductors. They can only receive, store, or dissipate energy from a circuit rather than supplying energy. Resistors limit current flow and dissipate energy as heat. Capacitors store electric charge and energy in an electric field. Inductors store energy in a magnetic field produced by current flowing through a coil. The key parameters are resistance (R) for resistors, capacitance (C) for capacitors, and inductance (L) for inductors.
Passive Circuit Components
- 1. PASSIVE CIRCUIT COMPONENTS Efforts By – SAKSHAM KOUL
- 2. PASSIVE CIRCUIT COMPONENTS – WHAT? A passive component is an electronic component which can only receive energy, which it can either dissipate, absorb or store it in an electric field or a magnetic field. Passive elements do not need any form of electrical power to operate. They are contrary in principle to the active circuit elements, which can be understood as suppliers of energy in a circuit, such as a battery. For Example: Resistor, Capacitor, Inductor etc…
- 3. RESISTOR A resistor is a passive electrical component with the primary function to limit the flow of electric current. The resistance of a resistor is its primary parameter. Resistance is expressed in Ohms (Ω) and is dependent on the shape of the resistive part and the material properties. A resistor is taken as a passive element since it can not deliver any energy to a circuit. Instead a resistor can only receive energy which it can dissipate as heat as long as current flows through it.
- 4. CircuitViewpoint EnergyViewpoint GeometricalViewpoint o By Ohm’s Law, we have 𝑅 = 𝑉 𝐼 o Resistance of most metallic conductors varies with temperature. 𝑅2 = 𝑅1 1 + 𝛼 𝑇2 − 𝑇1 Where, 𝑅1 - Resistance at temperature 𝑇1 𝑅2 - Resistance at temperature 𝑇2 𝛼 –Temperature coefficient of resistance o It converts electrical energy into heat energy. 𝑃 = 𝑉𝐼 = 𝐼𝑅 𝐼 = 𝐼2 𝑅 = Rate of energy absorbed The corresponding amount of energy converted to heat in the time interval 𝑡2 − 𝑡1 is given by – 𝑤 = 𝑡1 𝑡2 𝐼2 𝑅 ⅆ𝑡 o For constant current, this takes the form – 𝑤 = 𝐼2 𝑅𝑡 Where 𝑡 = 𝑡2 − 𝑡1 o 𝑅 = 𝜌 𝐿 𝐴 Where, 𝜌 – Resistivity / Specific resistance of the material 𝐿 – Length of the conductor 𝐴 – Cross-sectional area o Conductance is defined as the reciprocal of resistance. It is denoted by 𝐺 and is measured in siemens. 𝐺 ≡ 1 𝑅 Hence, 𝐺 = 1 𝜌 𝐴 𝐿 = 𝜎 𝐴 𝐿 𝜎 denotes conductivity and is the reciprocal of resistivity.
- 5. CAPACITOR A capacitor in an electrical circuit behaves as a charge storage device. It holds the electric charge when a voltage is applied across it, and it gives up the stored charge to the circuit as and when required. A capacitor is considered as a passive element because it can store energy in it as electric field. As such it is not considered an active component since no energy is being supplied or amplified. The capacitance of a capacitor is its primary parameter. Capacitance is expressed in Farads (F).
- 6. CircuitViewpoint EnergyViewpoint GeometricalViewpoint o Charge between two conducting metal surfaces is proportional to the potential difference between them, the proportionality constant is the capacitance 𝐶 i.e. 𝑞 = 𝐶𝑉 o The current flowing in the circuit is the rate of change of charge i.e. 𝐼 = ⅆ𝑞 ⅆ𝑡 = 𝐶 ⅆ𝑉 ⅆ𝑡 o Hence, the voltage across a capacitor cannot change instantaneously (in zero time). o The energy delivered to an uncharged capacitor by a current 𝐼 in time 𝑡 is given by 𝑤 = 0 𝑡 𝑉𝐼 ⅆ𝑡 𝑤 = 0 𝑡 𝑉 𝐶 ⅆ𝑉 ⅆ𝑡 ⅆ𝑡 = 0 𝑉 𝐶𝑉 ⅆ𝑉 Or 𝑤 = 1 2 𝐶𝑉2 o This energy is stored by the capacitor in an electric field existing between its two plates. o When the voltage across a capacitor is constant, there can be no current flow but energy is stored. o From Gauss’ Law, charge accumulated on the plates of a parallel plate capacitor can be written in terms of electric field 𝐸 as – 𝑞 = 𝜖𝐴𝐸 = 𝜖𝐴 𝑉 ⅆ 𝐶𝑉 = 𝜖𝐴 𝑉 𝑑 or 𝐶 = 𝜖𝐴 𝑑 o Hence, capacitance is directly proportional to the permittivity of the material between the plates and to the plate surface area, and is inversely proportional to the spacing between the plates.
- 7. INDUCTOR An inductor is an energy storage device which stores energy in the form of magnetic field when electric current flows through it. An inductor is also considered as a passive element of circuit, because it can store energy in it as magnetic field. Due to the property of induced emf, all types of electrical coils can be referred to as inductors. The inductance of an inductor is its primary parameter. Inductance is expressed in Henry (H).
- 8. CircuitViewpoint EnergyViewpoint GeometricalViewpoint o The induced emf across a coil is directly proportional to the rate of change of current through it, the proportionality constant is inductance 𝐿 i.e. 𝑉 = 𝐿 ⅆ𝐼 ⅆ𝑡 ⇒ 𝐿 = 𝑉 ⅆ 𝐼 ⅆ 𝑡 o Hence, the current in an inductor cannot change abruptly in zero time. o The energy delivered to an inductor having zero initial current by a current 𝐼, in time 𝑡 is given by 𝑤 = 0 𝑡 𝑉𝐼 ⅆ𝑡 𝑤 = 0 𝑡 𝑉 L ⅆ𝐼 ⅆ𝑡 ⅆ𝑡 = 0 𝐼 L𝐼 ⅆ𝐼 Or 𝑤 = 1 2 𝐿𝐼2 o This energy is stored in the form of a magnetic field existing inside the inductor. o A constant current results in a zero voltage drop across the ideal inductor, but energy can still be stored in its magnetic field. o Using Faraday’s law of EMI, 𝑉 = 𝐿 ⅆ𝐼 ⅆ𝑡 = 𝑁 ⅆ𝜙 ⅆ𝑡 𝐿 = 𝑁 ⅆ𝜙 ⅆ𝐼 o Now, 𝜙 = 𝑚𝑚𝑓 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑟𝑒𝑙𝑢𝑐𝑡𝑎𝑛𝑐𝑒 = 𝑁𝐼 𝑅 And 𝑅 = 𝑙 𝜇𝐴 Hence, 𝐿 = 𝑁2 𝜇𝐴 𝑙 Where, 𝑙 – Mean core length 𝐴 – Cross-sectional area 𝑁 – Number of turns in the coil 𝜇 – Magnetic permeability of core