Determine the charges stored by the capacitors if the switch is closed for a long time, given th

Determine the charges stored by the capacitors if the switch...

Key Concepts

Capacitor Charging (Q = CV Relationship)

Capacitors store electrical energy in the form of charge, and the relationship between the stored charge (Q), capacitance (C), and the voltage (V) across the capacitor is given by Q = CV. This fundamental principle is used to understand how much charge is accumulated when a voltage is applied over time.

Transient Analysis in RC Circuits

When a switch in a circuit is closed, the circuit initially undergoes a transient response as the capacitors charge, following an exponential behavior determined by the RC time constant. Over time, the circuit approaches steady state, where, in DC circuits, the capacitors effectively act as open circuits.

Steady-State Behavior in DC Circuits

After a sufficiently long time in a DC circuit, capacitors become fully charged and no more current flows in the circuit. The final charge on each capacitor is determined solely by the applied voltages and circuit configuration, regardless of the initial condition.

Effect of Switching on Circuit Configuration

Switching actions, such as closing or opening a switch, can dramatically alter the circuit configuration. Closing the switch allows a connection to a voltage source so that capacitors charge to prescribed equilibrium values, while opening the switch isolates portions of the circuit, preventing any charge redistribution or change from the initial state.

Transcript

00:01 So when the switch a is closed, all the charges is going through a capacitor 1.

00:07 Because when switch a is closed, only capacitor 1 exists in the circuits.

00:14 So therefore, we'll have the maximum amount of charge is just simply equal to the capacitance c1 times delta v.

00:24 Dlv is the potential difference across the battery, which is the potential difference across the circuits.

00:29 And windows c1 is equal to 15 microbarra and delta v is 100 volts.

00:36 So therefore, we have the maximum amount of charge is equal to 1 ,500 microcolon.

00:42 So now we switch the position.

00:46 So now switch b is close.

00:49 So once switch b is closed, the total amount of charges will start redistributing.

00:55 So therefore, since it's a parallel circuit, okay? so we have a maximum amount of charge should be equal to q1 plus q2.

01:05 Q1 is the amount of charge at capacitor 1, and q2 is the amount of charge at capacitor 2.

01:12 And q2 should be equal to q3, and q3 here is the amount of charge at capacitor 3.

01:17 It's because c2 and c3 are connected in series.

01:22 So we also know that the potential difference across capacitor 1 should be equal to the total of the potential difference at capacity 2 and the potential difference across capacitor 3, which is v1 is equal to v2 plus v3.

01:42 And we know potential difference, v1 here can be equal to q1 over c1, and v2 here can be able to q2 over c2, and v3 here can be equal to q3 over c3.

01:54 Because remember, potential can be able to charge over capacitance.

02:02 So therefore, we'll have q1 over c1.

02:05 Is also equal to q2 over c2 plus q2 over c3.

02:09 Because remember, q2 is equal to q3...

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