OBJECT: To determine the high resistance by method of leakage of chargeusing a Ballistic galvanometerAPPARTUS: A Ballistics galvanometer, Trainer kit , Lamp & scale arrangementstop watch, keys and a rheostat 600ohms .DIAGRAM

Theory

If a capacitor C is charged to a potential difference Vo is instantaneously discharged through a ballistic galvanometer giving rise to a first throw Ѳ0 then charge on the capacitor

Q0 =CVo= KQ0(1+ʎ/2)

Where k is the constant of the ballistic galvanometer and ʎ is the logarithmic decrement.

The capacitor is again charged to the same potential and the charge is allowed to leak through a high resistor R for a known time t so that potential falls from Vo to Vt.

If the remaining charge q on the capacitor is allowed to pass through the galvanometer so that a throw Ѳt is produced then.

Q=CVt=KѲt(1+ ʎ/2)

Hence

Qo/Q= Vo/Vt=Ѳo/Ѳt

If v is the potential difference across the capacitor at any instant during the time the charge is leaking and dQ/dt is the rate of loss of charge , then

I= - dQ/dt= -d/dt(CV)=-C(dV/dt)

Also

I=V/R

V/R=-C dV/dt

dt/RC=-dV/V

Interating for a time t we have

1/RC ∫0

t

dt=−∫0

t

dV /V

R=t

C . logeVOVT

=t

2.3026C . log10ѲOѲT

FORMULA: The resistance R of the given resistor is given by

t

2.3026C . log10ѲOѲT

Where,t= time for which the charge on the capacitor is allowed to leak through the highresistance RѲ0= first throw of the spot of light when the fully charged capacitor is dischargedthrough the Ballistic Galvanometer.Ѳt= first throw of the spot of light when the fully charged capacitor is firstdischarged through the resistance R for a time t and then discharged through theBallistics Galvanometer.C= capacity of the given capacitor in farads.PROCEDURELevel the ballistic galvanometer and set the lamp & scale arrangement. Adjust the position of the spot of light of the Galvanometer is adjusted at zero of the scale.Connect the trainer to the power supply mains.Make the battery switch Key K0 to on position.2. The connections are made as shown in the figure .Key k1 is made to position 1 and key k3 switched to position1 . It will charge the condenser.3. The key k3 is released from position 1 moved to position 2 . The first throw Ѳ0 is noted. The value of throw Ѳ0 is adjusted between 30 and 50 divisions with help ofrheostat.(connect a rheostat between the ballistic galvanometer if required)4. With the help of the damping key connected across the ballistic galvanometer , the motion of the galvanometer is stopped. Key k3 is pressed changed to 1 position to charge the condenser again by moving the K1 key to position1.5. Key k1 is removed from 1 and move to position1 and k2 is closed to short position. Same time start the stop watch. Key k3 is moved to position 1 for a time t second, say 10 second let the capacitor to discharge through the R. Then after 10 sec Turn the K3 Key position 2 to remaining charge to discharge through the ballistic galvanometer . The first throw Ѳt is noted.For the same value of Ѳ0 , Ѳt is observed for two more values of t.7. For a different set, the value of Ѳ0is changed by varying the resistance of therheostat and Ѳt is observed for three different values of t.

plot the graph taking the various values of time t along the x axis and the corresponding values of log10Ѳ0/ Ѳt . Find the slope of the curve and calculate the self leakage resistance r from the formula already given.

Similarly plot a graph between t and log10Ѳ0/ Ѳt and find the combined parallel resistance r’ of the combination r & R from which the resistance can be calculated