Energy Consumed in a Combined Resistor Circuit

Problem Statement

Consider a circuit with a DC power source (voltage $V$V, negligible internal resistance) connected to three resistors $R_1, R_2, R_3$R1​,R2​,R3​. Resistor $R_1$R1​ is connected in series with the power source, while resistors $R_2$R2​ and $R_3$R3​ are connected in parallel with each other after $R_1$R1​.

Find the Joule heat $Q_3$Q3​ generated in resistor $R_3$R3​ during time $t$t after the switch is closed.

Constraints

• Source voltage: $V = 48 \text{ V}$V=48 V
• Resistance 1: $R_1 = 4 \Omega$R1​=4Ω
• Resistance 2: $R_2 = 12 \Omega$R2​=12Ω
• Resistance 3: $R_3 = 6 \Omega$R3​=6Ω
• Time: $t = 15 \text{ s}$t=15 s

Input Format

Find the value of $Q_3$Q3​ and give the integer part of the answer (in units of $\text{J}$J).