Question

In the impedance triangle, why is the reactance of a capacitor negative and the reactance of an inductor positive?

Impedance Triangle Resistance (R) Where: Z-Impedance R- Resistance x,-X +X X,-Total Reactance X-Inductive Reactance Xc-Capacitive Reactance Impedance Reactano Reactance (Negative) Impedance円 Resistant* 5 Inductive and Capacitive Effects on Phase Angle

Answer 1

The impedance of a capacitor in given by the formula Z_c = 1/jwc = 1/j 2 pi fc then j = squareroot -1 It takes a bit of algebra to get the negative sign 1/j = j/j times 1/j = j/j^2 = j/-1 = -j so, z_c = 1/j times 1/wc = -j/wc Now, reactance in the imaginary part of the impedence, so, we can say X_c = ln{Z_c} = -1/wc This is negative Now come to the reactance of inductor X_L = jwL so, X_L = ln(Z_L) = wc This is positive This is the reason why reactance of capacitor in negative and reactance of a inductor is positive.