Final answer:
To achieve maximum power transfer to a resistor R in a circuit with resistors R1 and R2, R should be set equal to the equivalent resistance of R1 and R2, assuming they are in series. Therefore, R should be 62 Ω.
Step-by-step explanation:
To find the value of R for maximum power dissipation, we can apply the maximum power transfer theorem. This theorem states that maximum power is delivered to a load resistance (R) when the load resistance is equal to the internal resistance of the power source, including any resistances within the system.
In a network with R1 = 24 Ω and R2 = 38 Ω to achieve maximum power transfer to R, the value of R should be set equal to the equivalent resistance of R1 and R2. Assuming they are connected in series for this scenario, the equivalent resistance Req would be R1 + R2. So the value of R for maximum power dissipation would be 62 Ω.
However, if R2 is not in series with R1 and R, or the circuit configuration is not provided, additional information would be needed to find the value of R for maximum power transfer.