(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 galvanom...

(a) Magnetic flux pattern around a long straight current-carrying wire

The wire carries current out of the plane of the paper, as indicated by the dot. The magnetic field lines are concentric circles centred on the wire. Their direction is anticlockwise, given by the right-hand grip rule.

(b) The sensitivity of a moving-coil galvanometer can be increased by:

1. using a weaker control spring, so that the restoring torque is smaller;
2. using a stronger magnet to increase the magnetic flux density.

(c) Given: \(R=100\,\Omega\), \(L=3\,\text{H}\), \(C=4\,\mu\text{F}=4\times10^{-6}\,\text{F}\), \(V=100\,\text{V}\), and \(f=\dfrac{160}{\pi}\,\text{Hz}\).

(i) Series RLC circuit

(ii) Capacitive reactance

\[X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi\left(\dfrac{160}{\pi}\right)\left(4\times10^{-6}\right)}=781.25\,\Omega\]

\[\boxed{X_C\approx781\,\Omega}\]

(iii) Inductive reactance

\[X_L=2\pi fL=2\pi\left(\dfrac{160}{\pi}\right)(3)=960\,\Omega\]

\[\boxed{X_L=960\,\Omega}\]

(iv) Impedance

\[Z=\sqrt{R^2+(X_L-X_C)^2}\]

\[Z=\sqrt{100^2+(960-781.25)^2}=204.8\,\Omega\]

\[\boxed{Z\approx205\,\Omega}\]

(v) Current in the circuit

\[I=\frac{V}{Z}=\frac{100}{204.8}=0.488\,\text{A}\]

\[\boxed{I\approx0.49\,\text{A}}\]

(vi) Average power dissipated

Only the resistor dissipates average power:

\[P=I^2R=(0.488)^2(100)=23.8\,\text{W}\]

\[\boxed{P\approx24\,\text{W}}\]