Figure shows three resistor configurations $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ connected to $3 \mathrm{~V}$ battery. If the power dissipated by the configuration $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ is $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$, respectively, then

Figure:

A railway compartment is lit up by thirteen lamps each taking $2.1\, amp$ at $15\, volts$. The heat generated per second in each lamp will be ............ $cal$

A $4\,\mu F$ conductor is charged to $400\, volts$ and then its plates are joined through a resistance of $1\,k\Omega $. The heat produced in the resistance is ............... $J$

$(1)$  The product of a volt and a coulomb is a joule.

$(2)$  The product of a volt and an ampere is a joule/second.

$(3)$  The product of volt and watt is horse power.

$(4)$  Watt-hour can be measured in terms of electron volt.

State if

The figure shows a network of four resistances and three batteries The electrical power dissipated as heat is .............. $W$

A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.