JEE Advanced | 2014Current Electricity and Electrical InstrumentHard
Question
At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I0cos(ωt), with I0 = 1A and ω = 500 rad s-1 starts flowing in it with the initial direction shown in the figure. At t = 
, the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 μF, R = 10Ω and the battery is ideal with emf of 50 V, identify the correct statement(s).
, the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 μF, R = 10Ω and the battery is ideal with emf of 50 V, identify the correct statement(s).Options
A.Magnitude of the maximum charge on the capacitor before t = 
is 1 × 10-3C
is 1 × 10-3CB.The current in the left part of the circuit just before t = is clockwise
is clockwiseC.Immediately after A is connected to D, the current in R is 10 A
D.Q = 2 × 10-3C
Solution
The variation of current is shown below
The variation of current is shown below
Between t = 0 to
, charge will be maximum at 
Q =
I0 cosωtdt = 
(sin ωt)0π/2ω = 
= 2 × 10-3C
At t =
, sense of current will be opposite to initial sense i.e. anticlockwise.
At t =, the charge on upper plate is
I0 cosωtdt = 
[sin ωt]07π/6ω
× sin 
= - 10-3C
Applying KVL immediately after switch is shifted to D,
+ 50 +
- i × 10 = 0
Final charge on C after shifting the switch, Q′= CV = 20 × 10-6 × 50 = 10-3 C.
So, total charged flown from battery = 2 × 10-3C.
The variation of current is shown below
Between t = 0 to
, charge will be maximum at Q =
I0 cosωtdt = (sin ωt)0π/2ω = = 2 × 10-3CAt t =
, sense of current will be opposite to initial sense i.e. anticlockwise. At t =
, the charge on upper plate isI0 cosωtdt = [sin ωt]07π/6ω × sin = - 10-3CApplying KVL immediately after switch is shifted to D,
+ 50 +
- i × 10 = 0Final charge on C after shifting the switch, Q′= CV = 20 × 10-6 × 50 = 10-3 C.
So, total charged flown from battery = 2 × 10-3C.
Create a free account to view solution
View Solution FreeTopic: Current Electricity and Electrical Instrument·Practice all Current Electricity and Electrical Instrument questions
More Current Electricity and Electrical Instrument Questions
A micro ammeter has a resistance of 100 and a full scale range of 50 . It can used as a voltmeter or a higher range amme...A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance of...A cylindrical wire is stretched such that its length gets doubled but volume remains same, the resistance of wire become...A potential difference of 2V is applied between the opposite faces of a Ge crystal plant of area 1 cm2 and thickness 0.5...In the given circuit at t = 0 switch is on. Then after how much time voltage across resistance is 37 volt...