Q60 of 126 Page 198

Find the potential difference between the points A and B between the points B and C of figure in steady state.


Capacitors in parallel:


If capacitors C1, C2, C3 , … are in parallel, then the equivalent capacitance is given by:



Capacitors in series:


If capacitors C1, C2, C3 , … are in sereis, then the equivalent capacitance is given by:



Note that the charge is same on each capacitor in series in steady-state.


The circuit can be redrawn as follows:



We can see that C1 and C2 are in parallel,



Also, we can see that C3 and C24 are in parallel,



The circuit can be redrawn as follows:



Now, the two capacitors and are in series.




Note that there is no current in equilibrium. Hence,



As and are in series,





Now,





Also,





More from this chapter

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58

(a) Find the current in the 20 Ω resistor shown in figure.

(b) If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state?



 59

Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in figure.


 61

A capacitance C, a resistance R and an emf ϵ are connected in series at t = 0. What is the maximum value of

(a) the potential difference across the resistor,


(b) the current in the circuit,


(c) the potential difference across the capacitor,


(d) the energy stored in the capacitor,


(e) the power delivered by the battery and


(f) the power converted into heat.


 62

A parallel-plate capacitor with plate area 20 cm2 and plate separation 1.0 mm is connected to a battery. The resistance of the circuit is 10 kΩ. Find the time constant of the circuit.