Capacitor: Charging and Discharging Capacitor Explanation
18.1 CAPACITOR
18.1.1 Basic Components of a Capacitor
A capacitor is an electrical/electronic device which consists of two electrical conductors placed close to each other.
These conductors are separated from each other by a non-conducting material like air, plastic sheets, etc.
The conductors can be of any size and shape. For example, each conductor may be a small thin rectangular sheet of metal.
Each conductor in the capacitor may be referred to as a “plate”.
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18.1.2 Symbol Representing Capacitor
A fixed capacitor is represented by a pair of short parallel lines, as shown in Figure 18.1.
18.2 CHARGING AND DISCHARGING CAPACITOR
18.2.1 Charging a Capacitor
1. Charging current:
(a) Suppose we have a capacitor which is composed of two conducting plates, A and B, which are separated from each other by an insulating material. Then we connect a dc battery of emf E to the capacitor, as shown in Figure 18.2(a). The positive terminal of the battery is connected to plate A while the negative terminal is connected to plate B.
(b) Free negatively charged electrons in A are sucked out of plate A due to the positive potential at the positive terminal of the battery at the moment when the battery is connected to the capacitor. Electrons are pumped into plate B due to the negative potential at the negative terminal of the battery.
(c) In other words, at the moment when the battery is connected to the capacitor, electrons start to move in the external electric circuit. Electrons move out of A, travel through the battery and move into B. This movement of electrons produces an electric current in the circuit.
(Note: It is important to realize that the circuit as a whole is an open circuit because A and B are not in contact with each other. Yet there is a current flow in the external circuit. But there is no physical movement of free electrons from B to A since the region in between B and A is filled with an insulator.)
(d) As time passes, the magnitude of the current begins to decrease. Figure 18.2(b) shows how the current I varies with time t. Eventually, the current becomes zero. In other words, when a dc battery is connected to a capacitor, the battery will produce a current in the capacitor circuit, but this current only flows momentarily. Notice that the current starts flowing with a maximum value I₀.
(e) When the current stops flowing, plate A will have lost certain amount of negative charge and, as a result, it becomes positively charged. In the end it has “acquired” a positive charge, +Q. Plate B will have acquired the same amount of charge, −Q, but of the negative type.
(f) When current is still flowing in the circuit, the capacitor is said to be charging. But when the current has stopped flowing, the capacitor is said to have become fully charged.
(g) We say that a charged capacitor stores charge of amount, say, Q coulomb.
(h) We can show that the current decreases exponentially with time.
2. P.d. across capacitor while charging capacitor
(a) Initially the capacitor is uncharged, i.e., both A and B are neutral, so the p.d. across A and B is zero.
(b) When a dc battery is connected to the capacitor, A starts to lose electrons while B starts to acquire electrons. Because of this, A becomes positively charged while B becomes negatively charged.
(c) As time passes, A loses more electrons and becomes more positively charged. B acquires more electrons and becomes more negatively charged. Hence, the p.d. across A and B will increase with time.
(d) Figure 18.2(c) shows how the p.d. V across the capacitor varies with time t. Notice that at time t₀, when the current stops flowing, the p.d. reaches a maximum value, which is equal to the emf E of the battery.
(e) When the p.d. across the capacitor becomes equal in magnitude to the emf of the battery, the p.d. and the emf cancel each other. Hence, the effective net voltage across the capacitor is zero. This is the reason why the current has to stop flowing.
(f) We can show that the p.d. increases exponentially with time.
Summary
- (a) A dc battery connected to an uncharged capacitor produces a charging current in the capacitor circuit.
- (b) The current starts flowing in the circuit with a maximum value I₀.
- (c) The current then decreases exponentially with time and finally becomes zero.
- (d) When current stops flowing, the capacitor is said to have become fully charged. The charged capacitor now stores certain amount of charge.
- (a) Initially, the p.d. across the uncharged capacitor is zero.
- (b) As the capacitor becomes charged, the p.d. across the capacitor increases.
- (c) The p.d. increases exponentially with time.
- (d) Finally the p.d. reaches a maximum value which is numerically equal to the emf of the battery. At the same time the current stops flowing.
18.2.2 Discharging a Charged Capacitor
(a) Discharging current
(i) Suppose that we remove the dc battery from the fully charged capacitor. Since the capacitor is charged, a p.d. exists across A and B. A is positively charged while B is negatively charged.
(ii) Next we use a wire to connect electrically A to B. Free electrons immediately begin to flow out of B and electrons begin to flow into A.
as shown in Figure 18.3(a). Notice that the electrons now flow in the direction opposite to that of the charging current.
(iii) The movement of electrons in the external circuit produces a current. The current decreases with time. Figure 18.3(b) shows how the current I varies with time t. The current starts with a maximum value I₀ and then decreases to zero. The negative value of I indicates that the current direction is opposite to that of the charging current.
(iv) We can show that the current decreases exponentially with time.
(v) When the current has stopped flowing, it means that A and B have finally become electrically neutral. The capacitor is said to have discharged completely. It no longer stores any more of the charge that it has acquired before.
(b) p.d. across capacitor while discharging
(i) As electrons flow out of B and into A, the amount of charge stored in each conductor begins to decrease with time. As a result, A will become less and less positively charged while B will become less and less negatively charged.
(ii) As time passes, A and B finally become electrically neutral and uncharged. The p.d. across them becomes zero.
(iii) Figure 18.3(c) shows how the p.d. V varies with time t. Notice that at the moment when the p.d. becomes zero, the current stops flowing.
(iv) We can show that the p.d. decreases exponentially with time.
Summary
- 1 (a) A charged capacitor will discharge if we connect a conductor across its two plates.
- (b) While the capacitor discharges, a current flows in the circuit.
- (c) The current decreases exponentially with time until it reaches zero.
- (d) Then the capacitor becomes electrically neutral.
- 2 (a) While the capacitor discharges, the p.d. across it decreases.
- (b) The p.d. decreases exponentially with time until it reaches zero.
18.2.3 Charge in Capacitor During Charging
1 Consider a capacitor AB which is being charged by a d.c. battery. At a particular instant, plate A has acquired charge +q while at the same time plate B has acquired charge −q, as shown in Figure 18.4(a).
Figure 18.4
2 As time passes, the amount of charge stored in each plate increases. Figure 18.4(b) shows how the amount of charge stored q increases with time.
3 When the capacitor becomes fully charged, it stores maximum charge Q (= +Q in A or −Q in B).
4 We can show that q increases exponentially with t.
Keyword: capacitor, capacitors, charging discharging, capacitor definition, charging capacitor explanation, discharging capacitor process, capacitor current and voltage, RC circuit explanation, exponential charging capacitor
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