A resistor of resistance R is connected to a power supply of constant EMF E=12 V and internal resistance r=3 Ω . The energy dissipated in the resistor R is used to heat water. What resistance R in Ohms gives the maximum power dissipated in the resistor?
R = r = 3 Ohms.
To find the resistance value R that gives the maximum power dissipated in the resistor, we can use the formula for power:
P = (EMF^2 * R) / (R + r)^2
where P is the power, EMF is the electromotive force (or voltage), R is the resistance, and r is the internal resistance.
To maximize the power dissipated, we need to differentiate this equation with respect to R and set it equal to zero:
dP/dR = (EMF^2 * (r - R)) / (R + r)^3 = 0
Simplifying the equation, we have:
r - R = 0
Therefore, to maximize power dissipation, the resistance R should be equal to the internal resistance r.
In this case, the internal resistance r is given as 3 Ω, so the resistance R that gives maximum power dissipation would also be 3 Ω.