You are provided with a battery of e.m.f. E, a key K, a voltmeter, a standard resistor R\(_{0}\) = 2\(\Omega\), a resistance box R, and some connecting wires. i. Measure and record the e.m.f. E of the battery. i. Set up a circuit as shown in the diagram above with the key open. iii. Set the resistance on the resistance box to R 22. iv. Close the key, read and record the potential difference V on the voltmeter. v. Evaluate V\(^{-1}\) vi. Repeat the procedures for five other values of R = 5\(\Omega\) 10\(\Omega\),12\(\Omega\),15\(\Omega\) and 20\(\Omega\). In each case, record V and evaluate V\(^{-1}\) vii. Tabulate the results. viii. Plot a graph with R on the vertical axis and V\(^{-1}\) l on the horizontal axis, starting both axes from the origin (0,0). ix. Determine the slope, s, of the graph and the intercept c on the vertical axis. x. Calculate \(\propto\) and \(\beta\) from the equations s = R\(_{0}\) \(\propto\) and c= - (R\(_{0}\)+B). xi. State two precautions taken to obtain accurate results.
Explanation
R\(_{0}\) = 2\(\Omega\), emf of the battery = 2.0V Table of value
S/N
R\(\Omega\)
V
V
123456
2510121520
4.702.401.751.401.100.76
0.2140.4170.5710.7140.9091.320
Slope = \(\frac{\bigtriangleup R}{\bigtriangleup V^{-1}}\) = \(\frac{30.00-0.00}{1.50-0.15}\) = \(\frac{30.00}{1.35}\) = 22 Intercept on the horizontal axis = 0.15 Calculation of \(\propto\) \(\propto\) = \(\frac{S}{R_0} = \frac{22}{2}\) = 11 Calculation of \(\beta\) \(\beta\) = -(R\(_{0}\) + C) = - (2 + 0.15) = -(2.15) = -2.15 Precuations - Key opened in between reading/key opened when readings were not taken. - Tight connections ensured - Avoided parallax error when taking reading on voltmetre - Repeated readings shown on table - Noted/corrected zero error on voltmetre - Clean terminals ensured. (b) i. R\(_{AB}\) = \(\frac{4 \times 5}{4+5} = \frac{20}{9}\) P\(_{AB}\) =\(\frac{V_{AB^2}}{R_{AB}}\) = \(\frac{4^2 \times9}{20}\) = 7.2 W ii. I = \(\frac{p}{v}\)=\(\frac{3.6\times10^3}{240}\) = 15A The breaker will not open since the current drawn (15A) is less than (20A).
