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Combining what we have learnt in previous articles, opens up a whole new set of ideas to explore. The combination of Resistor and Capacitors results in an RC Circuit. One of the very important type of electronic circuits to be studied due to their wide range of applications.
Table of Contents :
- Basics of RC Circuits – Charging and Discharging
- Derivation (for Interested Readers) – Recommended
- Time Constant & It’s Importance
1. Basics of RC Circuit :
Charging without Resistor
Let’s consider a circuit with a battery of emf ‘E’ and a capacitor (capacitance ‘C’) connected in series to it via a switch ‘S’. Note that Capacitor is uncharged initially.
We know, charging will start as soon as the Switch ‘S’ is closed and also it is seen that the capacitor gets charged very quickly. This is shown in Fig.2 where we plot the charge v/s time graph in order to keep a track of the charge appearing on capacitor plates w.r.t time
- When we say that capacitor is fully charged, it means that, the capacitor plates have got the maximum charge they can hold. In this case it will be ‘CE’. Also this state where the charge doesn’t change anymore is called ‘Steady State‘
- As the charge keeps on developing on the capacitor, the current in the circuit keeps on decreasing till it becomes zero at steady state. This whole situation where every parameter(charge, current) is going under a change is called ‘Transient state‘
What happens when Resistance is added ?
Charging with Resistor
Now, we add a resistor with resistance R in series with the capacitor. Capacitor is uncharged initially. We have the most basic RC Circuit possible for analysis.
- We can sum up the role of resistor here in simple words. It is mainly used to increase the charging time of the capacitor. This makes the transient state to last a little longer. How long ?, can be decided and pre-calculated on the basis of R and C values chosen to build the resultant RC circuit.
In case of Charging, you can imagine Resistor as an cunning friend who doesn’t want you(capacitor) to grow in his/her life. This friend somehow tries to delay the work which you would have achieved very easily earlier.
Discharging without Resistor :
Consider we have a capacitor, fully charged with the help of battery of emf ‘E’ and we need to discharge it.
- This can be done by simply disconnecting the battery and then allowing the two plates of capacitor to be connected to each other.
- Similar to the charging process, the discharging of capacitor also happens instantly in absence of Resistor. This can be seen in the plot in Fig.7
Discharging with Resistor :
- In case of discharging, Resistor increases the discharging time . We can say that, Resistor here acts as a good friend who doesn’t allow you(capacitor) to fall(discharge) immediately.
Discharging still happens, but at a slower rate. This can be observed from the plot between q (charge on capacitor plate) v/s time ‘t’ as shown below.
So we can clearly see from Fig.8 that it takes time to reach 0 charge (for practical purpose). But how much time it takes, is decided by the R and C values
2. Derivations :
We see some non-linear curves in case of RC charging (Fig. 4) and in case of RC discharging (Fig. 8). But what is the nature of these graphs. How do we plot them exactly ? What is the equation. Let’s answer all of these through our Analysis
RC Charging :
RC Discharging :
3. Time Constant & It's Importance :
We represent ‘Time Constant’ by the greek letter ‘Tau’
- Time Constant is mainly formulated as the product of the Resistance and the Capacitance. It’s an important representation mainly used in RC(resistance-capacitance) and RL (resistance-inductance) circuits.
Now that we know, how it is formulated, replace R X C with time constant.
Let's start with Charging case :
- From the above analysis, We can define time constant (For charging) as the time required to charge the capacitor to 63% of the total charge it can achieve i.e. 63 % of the steady state charge
Let's discuss Discharging case :
- Again, from the above analysis, We can define time constant (For discharging) as the time required to discharge the capacitor to 37% of the total charge it had initially i.e. 37 % of the steady state charge
We can keep on inserting such time values and keep a track of the charge on capacitor.
Important : Note that q is the charge on the capacitor plates at time instant ‘t’
Charging case :
- It is seen that approximately after minimum (t = 5 * time constant), the capacitor is 99% charged. We consider that as approx fully charged in reality while doing some projects and all !
Discharging case :
- It can be seen again from the calculations below that, –> It takes about (t = 5 * time constant) in order to discharge the capacitor to an extent where only 1% of the initial charge remains on the plates.
- We consider this as approx. fully discharged case for project purposes
Conclusion :
So based on our previous articles knowledge (Resistors and Capacitors), we have learnt about the basics of RC Circuits. There will be another article to go into further depth in case of RC Circuits
- Have a look at the derivations, as those will provide a proper insight and reasoning of why exactly things happen in that way. It’s always good to have a look at the mathematical analysis of the physics concept you study !
Keep Learning !
