Answer:
r = 1 Ohms
Explanation:
Given that:
P = [tex]\frac{49r}{(r+0.8)^{2} }[/tex]
where r is the resistance in the circuit.
If r = 1 Ohms;
P = [tex]\frac{49(1)}{(1+0.8)^{2} }[/tex]
= [tex]\frac{49}{1.8^{2} }[/tex]
= [tex]\frac{49}{3.24}[/tex]
= 15.1235
P = 15.12 W
If r = 3 Ohms;
P = [tex]\frac{49(3)}{(3+0.8)^{2} }[/tex]
= [tex]\frac{147}{14.44}[/tex]
P = 10.18 W
If r = 5 Ohms;
P = [tex]\frac{49(5)}{(5+0.8)^{2} }[/tex]
= [tex]\frac{245}{33.64}[/tex]
= 7.230
P = 7.23 W
Therefore, the value of r for maximum power is 1 Ohms.
