Single phase $4$ pole pool pump motor delivering $1$hp of m$.$power is supplied using $240$VAC $($RMS$)$ and operates at power factor of $0\mathrm{.}96$ lagging. if the motor operates at $3\mathrm{.}8\%$ slip & is $85\%$ efficient.

a$)$ what is the torque delivered by motor?

b$)$ what is the impedance of the motor windings expressed as a phasor?

c$)$ what is the resistance and the inductance of the motor windings in ohm and henrys respectively?

d$)$ what impedance would be placed in parallel with the motor in order to increase the power factor to equal to $1?$ what would be the components type and its value?