Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is \( 0.5 \, \text{mm} \). The circular scale has \( 100 \) divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.
What are the diameter and cross-sectional area of the wire measured using the screw gauge?
As shown in the figure, the resistance of a galvanometer \( G \) can be found by the half-deflection method. Here the resistance \( R_2 \) is adjusted such that when the key \( K \) is closed the deflection in the galvanometer becomes half of the value as compared to when \( K \) is open. Half-deflection is obtained at \( R_2 = 4\,\Omega \) and thus the galvanometer resistance is found to be \( 6\,\Omega \). In this half-deflection condition the current (in \( \text{mA} \)) through the resistor \( R_1 \) is ________. 
