Capacitance, Current and Resistance, Lecture notes of Basic Electronics

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Capacitance,

Current and Resistance

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Capacitance

The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between the conductors:

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capacitance is always a positive quantity

The SI unit of capacitance is the farad (F), which was named in honor of Michael Faraday

1 F = 1 C/V

The farad is a very large unit of capacitance. In practice, typical devices have capacitances ranging from microfarads (10-6^ F) to picofarads (10-12^ F).

Example 1. Parallel-Plate Capacitor

(Example 26.1 Raymond)

A parallel-plate capacitor with air between the plates has an area A = 2.00 x 10-4^ m^2 and a plate separation d = 1.00 mm. Find its capacitance.

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Combinations of Capacitors

Two or more capacitors often are combined in electric circuits. We can calculate the equivalent capacitance of certain combinations using methods described in this section. Throughout this section, we assume that the capacitors to be combined are initially uncharged.

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Parallel Combination

the individual potential differences across capacitors connected in parallel are the same and are equal to the potential difference applied across the combination.

Example 2. Equivalent Capacitance

(Example 26.4 Raymond)

Find the equivalent capacitance between a and b for the combination of capacitors shown in Figure. All capacitances are in microfarads.

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Example 3. (Sample Problem 25.03, Halliday)

Capacitor 1, with C 1 = 3.55 μF, is charged to a potential difference V 0 = 6.30 V, using a 6.30 V battery. The battery is then removed, and the capacitor is connected as in Fig. to an uncharged capacitor 2, with C 2 8.95 μF. When switch S is closed, charge flows between the capacitors. Find the charge on each capacitor when equilibrium is reached.

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Resistance

resistance has SI units of volts per ampere. One

volt per ampere is defined to be one ohm (Ω)

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Most electric circuits use circuit elements called

resistors to control the current level in the

various parts of the circuit.

Resistance

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• for many materials (including most metals), the ratio of the current density to the electric field is a constant σ that is independent of the electric field producing the current.
• The resistance as the ratio of the potential difference across a conductor to the current in the conductor:
• The resistance has SI units of volts per ampere. One volt per ampere is defined to be one ohm (Ω). if a potential difference of 1 V across a conductor causes a current of 1 A, the resistance of the conductor is 1 Ω.
• The inverse of conductivity is resistivity^3 ρ: ρ 㐄 σ^ l , where

ρ has the units ohm-meters (Ω.m). Because R㐄 ρ (^) σAl we can express the resistance of a uniform block of material along the length ᡤ as R㐄 ρ (^) Al

Electrical Power

• The rate at which the system loses potential energy as the charge passes through the resistor is equal to the rate at which the system gains internal energy in the resistor. Thus, the power P, representing the rate at which energy is delivered to the resistor, is :
• ∆V㐄I.R for a resistor, we can express the power delivered to the resistor in the alternative forms

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Example 6. Power in an Electric Heater (Example 27.7 Raymond)

An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the current carried by the wire and the power rating of the heater.