To measure the supply frequency using series resonant circuit

Aim of the experiment : To measure the supply frequency using series resonant circuit. 

Apparatus Required : 

SL.No.	Name of the apparatus	Range	Make	Make No.	Quantity
1.	Supply source	0-30v, AC			1
2.	Ammetre	0-100mA			1
3.	Voltmeter	0-50v			1
4.	Resistance	25 ohm			1
5	Inductance	1-10 H			1
6.	Capacitance	3 micro Farad			1

Theory : 

       We know that-

         Impedance, Z= √{R2+(X L - X C)2}

         Where X L=WL & X C=1/WC

         when X L=X C then Z=R

          =>WL=1/WC

          =>W2=1/LC

          =>W=1/√LC

          =>2πfr=1/√LC

          =>f r =1/2π√LC

Here,  f r is called resonant frequency and phenomenon is called series resonance.

Circuit Diagram : 

 

                              Fig : (1)
Procedure : 

1.Connected  the circuit as per the circuit diagram. 

2.Kept  supply voltage constant at 30v

3.keeping the value of capacitance constant,  increased the value of inductance stepwise.

4.Noted down the different reading of ammeter. 

observation Table : 

SL. No.	Ammeter value(mA)	C(micro Farad)	L(H)	Value of L at I max(H)	f0(Hz)	% Error
1.	37	3	1
2.	43	3	2
3.	46.5	3	3
4.	47	3	4	4	45.944	8.112%
5.	44	3	5

formula used : 

    f r =1/2π√LC

    

   % Error = {(Theoretical value - practical value) / (Theoretical value) }*100

Graphs : 

                      

                      

Precautions : 

1.All the connections should be properly tightened.

2. The ammeter should be checked for their zero positions before connection.

3.The connections should be verified by the lab.  technician before switching the switch. 

Results : The supply frequency and The percentage error for the experiment is 45.944 Hz & 8.112% respectively.

Conclusion : The reasons for the % error in the experiment is 

 A.We have not considered the resistance in the wires. 

B.The devices we used may have some error.