A resistor of unknown value $x$ is connected in parallel to a $20$ resistor. This combination is then connected in series to another parallel combination with a $30$ and a $50$ resistor. The circuit is supplied from a $110$ V supply.

Calculate the value of the unknown resistor if the current through the $50$ resistor is $2$ A$.$ Also, calculate the energy dissipated by the unknown resistor in $36$ seconds.

A $90F$ capacitor is connected in parallel with a $40F$ capacitor. This parallel combination is then connected in series with another parallel combination of a $70F$ and $35F$ capacitor. If the circuit is connected across a $110$ V DC supply, calculate:

$1\mathrm{.}3\mathrm{.}1$ The total capacitance of the circuit.

$1\mathrm{.}3\mathrm{.}2$ The potential difference across each parallel branch.

$1\mathrm{.}3\mathrm{.}3.$The charge across each capacitor