Calculate R, V, R1=202, R2=502 Series and Parallel Calculation

Question

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for total power (P) for both series and parallel configurations.

Given:
$V_T = 24 \, \text{V}$
$R_1 = 20 \, \Omega$
$R_2 = 50 \, \Omega$

Series Circuit Calculation

Calculate the total resistance ( $R_T$ ) for resistors in series.
$R_T = R_1 + R_2$ $R_T = 20 \, \Omega + 50 \, \Omega$ $R_T = 70 \, \Omega$
Calculate the total current ( $I_T$ ) using Ohm's Law.
$I_T = \frac{V_T}{R_T}$ $I_T = \frac{24 \, \text{V}}{70 \, \Omega}$ $I_T = \frac{12}{35} \, \text{A} \approx 0.343 \, \text{A}$
Calculate the total power ( $P_T$ ) for the series circuit.
$P_T = V_T \cdot I_T$ $P_T = 24 \, \text{V} \cdot \frac{12}{35} \, \text{A}$ $P_T = \frac{288}{35} \, \text{W}$ $\boxed{P_T \approx 8.23 \, \text{W}}$
Parallel Circuit Calculation
Calculate the total resistance ( $R_T$ ) for resistors in parallel.
$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ $\frac{1}{R_T} = \frac{1}{20 \, \Omega} + \frac{1}{50 \, \Omega}$ $\frac{1}{R_T} = \frac{5}{100 \, \Omega} + \frac{2}{100 \, \Omega}$ $\frac{1}{R_T} = \frac{7}{100 \, \Omega}$ $R_T = \frac{100}{7} \, \Omega \approx 14.29 \, \Omega$
Calculate the total current ( $I_T$ ) using Ohm's Law.
$I_T = \frac{V_T}{R_T}$ $I_T = \frac{24 \, \text{V}}{\frac{100}{7} \, \Omega}$ $I_T = \frac{24 \times 7}{100} \, \text{A}$ $I_T = \frac{168}{100} \, \text{A} = 1.68 \, \text{A}$
Calculate the total power ( $P_T$ ) for the parallel circuit.
$P_T = V_T \cdot I_T$ $P_T = 24 \, \text{V} \cdot 1.68 \, \text{A}$ $P_T = 40.32 \, \text{W}$ $\boxed{P_T = 40.32 \, \text{W}}$

Answer