(a) Derive the relation between commercial unit of energy (kWh) and SI unit of energy (joule).
(b) A certain household consumes 650 units of electricity in a month. How much is this electricity in joules?

(a). Derivation of the relation between (kWh) and (Joule):

$1\ kWh=1\ kW\times 1\ hour$

$=1000\ Watt\times 60\times60\ seconds$

$=3.6\ 10^6\ Watt-seconds$

$=3.6\times10^6\ Joule$

Therefore, $1\ kWh$ is equal to $3.6\times10^6\ Joule$.

(b). Electricity used in household $=650\ units$

$=650\ kWh$            [commercial unit of power is $kWh$]

$=650\times3.6\times10^6\ Joule$

$=2340\times10^6\ Joule$

$=23.4\times10^7\ Joule$