Alexander-Sadiku
Fundamentals of Electric Circuits

	Chapter 6
	Capacitors and Inductors

Capacitors and Inductors Chapter 6

	6.1 Capacitors
	6.2 Series and Parallel Capacitors
	6.3 Inductors
	6.4 Series and Parallel Inductors

6.1 Capacitors (1)

	A capacitor is a passive element designed        to store energy in its electric field.

6.1 Capacitors (2)

	Capacitance C is the ratio of the charge q on one plate of a capacitor to the voltage difference v between the two plates, measured in farads (F).

6.1 Capacitors (3)

	If i is flowing into the +ve terminal of C
		Charging => i is +ve
		Discharging => i is –ve

6.1 Capacitors (4)

	The energy, w, stored in the capacitor is

6.1 Capacitors (5)

	Example 1
		The current through a 100-mF capacitor is
		i(t) = 50 sin(120 pt) mA.
		Calculate the voltage across it at t =1 ms and
		t = 5 ms.
		Take v(0) =0.

6.1 Capacitors (6)

	Example 2
		An initially uncharged 1-mF capacitor has the current shown below across it.
		Calculate the voltage across it at t = 2 ms and
		t = 5 ms.

6.2 Series and Parallel
Capacitors (1)

	The equivalent capacitance of N parallel-connected capacitors is the sum of the individual capacitances.

6.2 Series and Parallel
 Capacitors (2)

	The equivalent capacitance of N series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.

6.2 Series and Parallel
Capacitors (3)

	Example 3
	Find the equivalent capacitance seen at the terminals of the circuit in the circuit shown below:

6.2 Series and Parallel
Capacitors (4)

	Example 4
	Find the voltage across each of the capacitors in the circuit shown below:

6.3 Inductors (1)

	An inductor is a passive element designed         to store energy in its magnetic field.

6.3 Inductors (2)

	Inductance is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

6.3 Inductors (3)

	The current-voltage relationship of an inductor:

6.3 Inductors (4)

	Example 5
	The terminal voltage of a 2-H    inductor is
		v = 10(1-t) V
	Find the current flowing through it at    t = 4 s and the energy stored in it within 0 < t < 4 s.
	Assume i(0) = 2 A.

6.3 Inductors (5)

	Example 6
	Determine vc, iL, and the energy stored in the capacitor and inductor in the circuit of circuit shown below under dc conditions.

6.4 Series and Parallel
 Inductors (1)

	The equivalent inductance of series-connected inductors is the sum of the individual inductances.

6.4 Series and Parallel
Inductors (2)

	The equivalent capacitance of parallel inductors is the reciprocal of the sum of the reciprocals of the individual inductances.

6.4 Series and Parallel
 Capacitors (3)

	Example 7
	Calculate the equivalent inductance for the inductive ladder network in the circuit          shown below:

6.4 Series and Parallel
Capacitors (4)

	Current and voltage relationship for R, L, C