a What is the greatest voltage that the battery can have wit

(a) What is the greatest voltage that the battery can have without one of the resistors burning up?
_____________V

(b) How much power does the battery deliver to the circuit in (a)?
______________W

Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 1.8 ? and 3.6 W, 11.3 ? and 9.5 W, and 3.2 ? and 5.2 W.

Solution

R_{series(total)} = R₁ + R₂ + R₃ = (1.8+11.3+3.2) ohms = 16.3 ohms

Max allowed voltage drop across each is ? (W . R)

for 1.8 ohms and 3.6W ....... V= ? (1.8*3.6)V = 2.5 V and maximum current = 1.4 A

for 11.3 ohms and 9.5W.... V=?(11.3*9.5)V = 10.36 V and maximum current = 0.92 A

for 3.2 ohms and 5.2 W... V= ?(3.2*5.2)V = 4.079 V and maximum current = 1.27 A

Max current through the circuit must be 0.92 A and so the Max battery voltage is I . R(total)

V= I * R_(total) = 0.92 * 16.3= 14.996 Volts