A 13-kg sled is moving at a speed of 3.0 m/s. At which of the following speeds will the sled have twice as much kinetic energy?
1 answer:
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Answer:
(A) Capacitance per unit length =
(B) The magnitude of charge on both conductor is C and the sign of charge on inner conductor is
and the sign on outer conductor is
Explanation:
Given :
Radius of inner part of conductor =
m
Radius of outer part of conductor =
m
The length of the capacitor =
m
(A)
Capacitance is purely geometrical property. It depends only on length, radius of conductor.
From the formula of cylindrical capacitor,
Where,
But we need capacitance per unit length so,
capacitance per unit length =
(B)
The charge on both conductors is given by,
Where, C = capacitance of cylindrical capacitor and value of F,
V
∴ C
The magnitude of charge on both conductor is same as above but the sign of charge is different.
Charge on inner conductor is and Charge on outer conductor is
.
Answer:
The fraction fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants is
Explanation:
From the question we are told that
The time constant
The potential across the capacitor can be mathematically represented as
Where is the voltage of the capacitor when it is fully charged
So at
Generally energy stored in a capacitor is mathematically represented as
In this equation the energy stored is directly proportional to the the square of the potential across the capacitor
Now since capacitance is constant at
The energy stored can be evaluated at as
Hence the fraction of the energy stored in an initially uncharged capacitor is