For the resistive circuit in Fig. 20.4,
a. Find the instantaneous power delivered to the resistor at times $t_1 through t_6$ .
b. Plot the results of part (a) for one full period of the applied voltage.
c. Find the average value of the curve of part (b) and compare the level to that determined by Eq. (20.3).

$P=VI=\frac{V_mI_m}{2}=I^2R=\frac{V^2}{R}\qquad (watts, W)\qquad (20.3)$
d. Find the energy dissipated by the resistor over one full period of the applied voltage.

Question

For the resistive circuit in Fig. 20.4,
a. Find the instantaneous power delivered to the resistor at times [latex]t_1 through t_6[/latex].
b. Plot the results of part (a) for one full period of the applied voltage.
c. Find the average value of the curve of part (b) and compare the level to that determined by Eq. (20.3).

[latex]P=VI=\frac{V_mI_m}{2}=I^2R=\frac{V^2}{R}\qquad (watts, W)\qquad (20.3) [/latex]
d. Find the energy dissipated by the resistor over one full period of the applied voltage.

Accepted Answer

a. [latex]t_1: \nu_R=0V\hspace{30 pt} and\hspace{30 pt} p_R = \nu_R i_R = 0 W\[0.5cm] t_2: \nu_R=12V\hspace{30 pt} and\hspace{30 pt} i_R=12V/4\Omega=3A\[0.5cm] p_R = \nu_Ri_R = (12 V)(3 A) = 36 W\[0.5cm] t_3: \nu_r=6V\hspace{30 pt}and\hspace{30 pt} i_R=6V/4\Omega=1.5A\[0.5cm] p_R = \nu_Ri_R = (6 V)(1.5 A) = 9 W\[0.5cm] t_4: \nu_R=0V\hspace{30 pt} and\hspace{30 pt} p_R = \nu_R i_R = 0 W\[0.5cm] t_5:\nu_R=-12V\hspace{30 pt} and\hspace{30 pt} i_R=-12V/4\Omega=-3A\[0.5cm] p_R = \nu_Ri_R = (-12 V)(-3 A) = 36 W\[0.5cm] t_6: \nu_R=0V\hspace{30 pt} and\hspace{30 pt} p_R = \nu_R i_R = 0 W [/latex]

b. The resulting plot of [latex]\nu_R, i_R, and p_R[/latex] appears in Fig. 20.5.

c. The average value of the curve in Fig. 20.5 is 18 W, which is an exact match with that obtained using Eq. (20.3). That is,

[latex]P=\frac{V_mI_m}{2}=\frac{(12 V)(3 A)}{2(1 kHz)}=18 mJ [/latex]

d. The area under the curve is determined by Eq. (20.5):

[latex]W_{R}=\frac{VI}{f_{1}}=\frac{V_{m}I{m}}{2f_{1}}=\frac{(12V)(3A)}{2(1KHz)}=18mJ[/latex]

Question 20.1: For the resistive circuit in Fig. 20.4, a. Find the instanta...

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