$A$ 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

The resistances in the following circuit are $R_1 = R_2 = R_3 = 6.0 \ \Omega$. The emf of the battery is $12 \ V$. When switch $S$ is closed, the potential across resistance $R_1$ changes by an amount:

Two wires $A$ and $B$ made of the same material and having their lengths in the ratio $6 : 1$ are connected in series. The potential differences across the wires are $3\,V$ and $2\,V$ respectively. If $r_A$ and $r_B$ are the radii of $A$ and $B$ respectively,then $\frac{r_B}{r_A}$ is

Two resistors of $100 \ \Omega$ and $200 \ \Omega$ are connected in series with a battery of $4 \ V$ and negligible internal resistance. $A$ voltmeter is used to measure the voltage across the $100 \ \Omega$ resistor,which gives a reading of $1 \ V$. The resistance of the voltmeter must be . . . . . . $\Omega$.

$A$ cell of emf $1.8 \ V$ gives a current of $17 \ A$ when directly connected to an ammeter of resistance $0.06 \ \Omega$. The internal resistance of the cell is: (in $\Omega$)

If the power dissipated in the $3\,\Omega$ resistor is $27\,W$,then what is the power dissipated in the $2\,\Omega$ resistor (in $,W$)?