A voltage of 230∠60° is applied to a current offering an impedance of 10 + j10 Ω. Find the expression for the current flowing through the circuit in polar form.

Conversion from rectangular form to polar form

The rectangular form of a coordinate is represented by \(x+iy\)

The polar form of a coordinate is represented by \(a∠\theta\)

where, \(a=√{x^2+y^2}\)

\(\theta=tan^{-1}({y\over x})\)

Calculation

Given, Voltage =  230∠60° 

Z = 10 + j10 Ω = 10√2∠45° 

\(I={V\over Z}\)

\(I={230\angle60 \over 10\sqrt{2}\angle 45}\)

I = 16.3∠15°

The voltage phasor is 230∠60° and current phasor is 16.3∠15°. Taking the voltage as the reference, the current will lag the voltage by 45 degrees with an amplitude of 16.3 Amp.

Additional Information Conversion from polar to rectangular form

The polar form of a coordinate is represented by \(a∠\theta\)

The rectangular form of a coordinate is represented by \(x+iy\)

where, \(x=acos\theta\)

\(y=asin\theta\)