1. The Energy Storage Elements
CHAPTER 5
The Energy Storage Elements

2. Q = CV The capacitor is a device that stores charge
The charge and the applied voltage are related
by the capacitance of the capacitor as
Q = CV
For a time varying source v(t) we have
q(t) =C v(t)
The unit of capacitance is coulomb/volt or Farad
For plates if size A (m2) separated by distance
d(m) with air in between the capacitance is:
C = 8.84×10¹²ֿ A/d F
Figure 5.1 A parallel-plate capacitor.

3. Passive sign convention

5. Capacitor Energy
The instantaneous power delivered to the capacitor is:
The energy stored in a capacitor at a particular time can be found by:
Assuming capacitor voltage is zero at

6. Example 5.1 A voltage source is applied to a 5-F capacitor as shown.
Sketch the capacitor current and the stored energy as a function of time.

9. Example 5.2 A current source is applied to a 5-F capacitor.
Sketch the capacitor voltage as a function of time.

10. The capacitor voltage is related to area Under current source.
For example area at t = 1 s is
Area of Triangle is (1)(10)=10
V(1s)=10/5= 2V.
For example area at t=3 s is = 25 hence
V(3s)=25/5= 5V.

11. 5.1.1 Capacitors in Parallel
The terminal voltage is equal to the voltage of each capacitors
v(t) = v1(t) = v2(t)=….=vn(t)
The current entering the combination is the sum of currents of each capacitor
i(t) = i1(t)+i2(t)+…+in(t)
From relation

12. 5.1.1 Capacitors in Series v(t) = v1(t) + v2(t) + …. + vn(t)
i(t) = i1(t) = i2(t) = … = in(t)

15. The Inductor A device that stores energy in its magnetic field
The current produces a magnetic field round the wire

16. The relation between the voltage and current of inductor is
This relation can be inverted to yield

17. The energy stored in an inductor
The instantaneous power of an inductor
Thus the energy stored in an inductor is

18. Example 5.3
A current source is applied to a 5-H inductor as shown. Sketch the voltage across the inductor versus time.

21. Example 5.4
A voltage source is applied to a 5-H inductor as shown. Sketch the inductor current versus time.

23. Inductors in Series

24. Inductors in Parallel

25. v(t)=2t <t<1
V(t)= -2t <t<2
iL=t2/ <t<1
iL= -t2/2+2t <t<2