The inductance of a certain moving-iron ammeter is expressed as $$L = 10 + 3\theta - {{{\theta ^2}} \over 4}\mu H,\,\,$$ where $$\,\,\theta \,\,\,$$ is the deflection in radians from the zero position. The control spring torque in $$\,\,25\,\, \times \,\,{10^{ - 6}}\,\,\,$$ Nm/radian. The deflection of the pointer in radian when the meter carries a current of $$5A,$$ is

An ac voltmeter uses the circuit shown below, where the $$PMMC$$ meter has an internal resistance of $$100$$$$\Omega $$ and requires a dc current of $$1$$ $$mA$$ for full scale deflection. Assuming the diodes to be ideal, the value of $${R_s}$$ to obtain full scale deflection with $$100$$ $$V$$ (ac rms) applied to the input terminal would be

The items in List $$-$$ $${\rm I}$$ represent the various types of measurements to be made with a reasonable accuracy using a suitable bridge. The items in List $$-$$ $${\rm II}$$ represent the various bridges available for this purpose. Select the correct choice of the item in List $$-$$ $${\rm II}$$ for the corresponding item in List $$-$$ $${\rm I}$$ from the following.

List $$-$$ $${\rm I}$$
$$A.$$ Resistance in the milli Ohm range
$$B.$$ Low values of Capacitance
$$C.$$ Comparison of resistances which are nearly equal
$$D.$$ Inductance of a coil with a large time $$-$$ constant

List $$-$$ $${\rm II}$$
$$1.$$ Wheatstone Bridge
$$2.$$ Kelvin Double Bridge
$$3.$$ Schering Bridge
$$4.$$ Wien's Bridge
$$5.$$ Hay's Bridge
$$6.$$ Carry $$-$$ Foster Bridge

The voltage-flux adjustment of a certain $$1$$-phase $$220$$ $$V$$ induction watt-hour meter is altered so that the phase angle between the applied voltage and the flux due to it $${85^0}$$ (instead of $${90^0}$$). The errors introduced in the reading of this meter when the current is $$5$$ $$A$$ at power factors of unity and $$0.5$$ lagging are respectively