Length of the wire remains same,
  

Magnetic moment of a coil, m = NAI

For the coil of radius R, magnetic moment, 

Magnetic moment for coil of radius R/2,

Therefore, 

When a capacitor is charged by a battery, work is done by the charging battery at the expense of its chemical energy. This work is stored in the capacitor in the form of electrostatic potential energy.

Consider a capacitor of capacitance C. Initial charge on capacitor is zero. Initial potential difference between capacitor plates =0. Let a charge Q be given to it in small steps. When charge is given to capacitor, the potential difference between its plates increases.

Potential difference between its plates, V= q/C

Work done to give an infinitesimal charge dq to the capacitor is given by, 
 

If V is the final potential difference between capacitor plates, then Q = CV

Work is stored in the form of electrostatic potential energy.
Electrostatic potential energy, U = 

When battery is disconnected,

i) Energy stored will decrease.

Energy becomes, U = 

So, energy is reduced to 1/K times its initial energy.

i) In the presence of dielectric, electric field becomes, E = 

We have,

Effective resistance between B and E is,


On applying Kirchoff's law, we have

Hence,
  

Suppose a resistance R, inductance L and capacitance C connected in series.
An alternating source of voltage V = V_o sin t is applied across it. Since all the components are connected in series, the current flowing through all is same.

Voltage across resistance R is V_R, voltage across inductance L is V_L and voltage across capacitance C is V_C.

V_R and (V_C -V_L) are mutually perpendicular and the phase difference between them is 90°.

From the figure above, we have 

and

The phase difference between current and voltage is given by, 
                              

From the graph, we can see that with increase in frequency, current first increases and then decreases. At resonant frequency, current amplitude is maximum.

The average time elapsed between two successive collisions is known as the relaxation time of free electrons drifting in a conductor.

Relation between  and v_d is given by, 
                    

Consider a conductor of length ‘l’, area of cross-section A and current density n.

Current flowing through the conductor is given by, 
         

Electric field applied across the ends is given by, E = V/l

So current flowing through the conductor becomes,
                       
Then, 

Using ohm's law, we get
 

Therefore,