A potentiometer, which consists of a driving cell connected to a resistance wire of length 100 cm, is used to compare the resistances of two resistors.

a. Draw a diagram to show the circuits that are used to compare the two resistances.

b. When resistor R₁ alone is tested the length of resistance wire for balance is 15.4 cm. There is an uncertainty in measuring the beginning of the resistance wire of 0.1cm, and in establishing the balance point of a further 0.1 cm.

i. Determine the uncertainty in the balance length. When R₁ and R₂ are tested in series the balance length is 42.6 cm. There are similar uncertainties in measuring this balance length.

ii. Calculate the ratio of  R₁/(R₁ +R₂).
iii. Calculate the value of the ration of  R₁/R₂ .

iv. Calculate the uncertainty in the value of the ratio R₁/R₂ .