Question

Consider the load convention that is used for the RLC elements shown in Figure 2.2 of the text

A. If one says that an inductor absorbs zero real power and positive reactive power, is it

(a) True

(b) False

B. If one says that a capacitor absorbs zero real power and negative reactive power (or delivers positive reactive power), is it

(a) False

(b) True

C. If one says that a (positive valued) resistor absorbs (positive) real power and zero reactive power, is it

(a) True

(b) False

Short answer

Answer

A. The correct option is (a) True

B. The correct option is (b) True

C. The correct option is (a) True

Step-by-step solution

Draw the impedance and power triangles for RL and RC series circuits.

Consider that the $R$ is a resistance, $X_L$is inductive reactance, $X_C$ is capacitive reactance, $Z$ is impedance and $I$is a current through the series RL and series RC circuits.

Draw the impedance and power triangles for series RL circuits

Figure 1: impedance and power triangle of series RL circuit

Draw the impedance and power triangles for series RC circuits

Figure 2: impedance and power triangle of series RC circuit

Solution for subpart A.

From power triangle of Figure 1, the total power is given by

$$\begin{gathered} P_{Total}=I^{2}R+j{I}^2{X}_L \\ =P+jQ \end{gathered}$$

Here, $P$is a real power and $Q$is a reactive power.

From impedance diagram of Figure 1, it is clear that the inductor absorbs reactive power and zero real power.

Thus the option (a) true is correct.

Solution for subpart B.

From power triangle of Figure 2, the total power is given by

$$\begin{gathered} P_{Total}=I^{2}R+j{I}^2{X}_L \\ =P+jQ \end{gathered}$$

Here,$P$is a real power and$Q$is a reactive power.

From impedance diagram of Figure 2, it is clear that the capacitor absorbs negative reactive power and zero real power.

Thus the option (b) true is correct.

Solution for subpart C.

C. From power triangle of Figure 1 and Figure 2, the real power is align to the x-axis.

From impedance diagram of Figure 1 and Figure 2, it is clear that the resistor only absorbs the real power.

Thus, the option true (a) true is correct.