(a) Sketch the magnetic flux pattern around a long; straight, current-carrying wire (b) State two methods by which the sensitivity of a moving-coil galvanometer can be increased. (c) A series RLC circuit comprises a 100-\(\Omega\) resistor, a 3-H inductor and a 4-\(\mu\)f capacitor. The a.c source of tile circuit has an e.m.f of 100V and a frequency of 160 Hz. (i) Draw the circuit diagram of the arrangement. Calculate the: (ii) capacitive reactance; (iii) inductive reactance: (iv) impedance of the circuit; (v) current in the circuit; (vi) average power dissipated in the circuit.
Explanation
(a)
(b) The sensitivity is increased by a weak spring and increasing the strength of the magnet C (c)(i)
(ii) X = \(\frac{1}{2 \pi FC} = \frac{1}{2 \pi \frac{160}{\pi} \times 4}\) = 781\(\Omega\) (iii) X\(_L\) = 2\(\pi\)fL = 2\(pi\) x \(\frac{160}{\pi}\) x 3 = 960\(\Omega\) (iv) Z = \(\sqrt{R^2 + (X_L - X_c)^2} = \sqrt{100^2 + (960 - 781)^2}\) = 205\(\Omega\) (v) I = \(\frac{v}{z} = \frac{100}{205} = 0.49A\) (vi) P = I\(^2R\) = (0.49)\(^{2}\) x 100 = 23.795 W = 24W
