Wheatstone's Bridge - 6

Medium:
1. In an experiment, values of two resistances are measured to be r₁ = (5.0 ± 0.2) and r₂ = (10.0 ± 0.1). Find the values of total resistance in parrallel with limits of percentage error.
Solution:- Combined resistance in parallel (R_P) is given by

R_P =

          = ± 0.07 (Relative error)
R_P = ± 7 %
         = (3.3 + 7 %)

2. Calculate the total length of a spherical mirror from the following observations: objects distance u = (50.1 ± 0.5) cm and image distance v = (20.1 ± 0.2) cm.
Solution:- As
                      f = = 14.3 cm
Also            
                           = ± [0.00998 + 0.00995 + 0.00997]
                           = ± 0.02990
                     f = 0.02990 x f = 0.0299 x 14.34 = 14.34 = 0.428 = 0.4 cm
                        f = (14.3 ± 0.4) cm

3. The time period of oscillation of simple pendulum is given by t = . What is the accuracy in the determination of g if 10 cm length is known to 1mm accuracy and 0.5 s time period is measured from time of 100 oscillations with a watch of 1 s resdution.
Solution:- Here
              t = 1 sec, and
time of 100 oscillation t = 100 x 0.5 = 50 s

from t =
        t² =
        g =

error 100 = ± 5 %

Keywords:
1. Specific heat.
2. Temperature.
3. Tripple point.
4. Thermal capacity.