The length of a wire of a potentiometer is $$100$$ $$cm$$, and the $$e.$$ $$m.$$ $$f.$$ of its standard cell is $$E$$ volt. It is employed to measure the $$e.m.f.$$ of a battery whose internal resistance in $$0.5\Omega .$$ If the balance point is obtained at $$1=30$$ $$cm$$ from the positive end, the $$e.m.f.$$ of the battery is

where $$i$$ is the current in the potentiometer wire.

An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ the value of the required shunt is

If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a

A wire when connected to $$220$$ $$V$$ mains supply has power dissipation $${P_1}.$$ Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $${P_2}.$$ Then $${P_2}:{P_1}$$ is