Three resistors are connected in series across a battery. The value of each resi

Question

Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 6.0? and 25.3 W, 31.5? and 11.7 W, and 18.3? and 14.4 W. (a) What is the greatest voltage that the battery can have without one of the resistors burning up? (b) How much power does the battery deliver to the circuit in (a)?

Explanation / Answer

P=I*U U=RI ==> I=U/R ==> P=U^2/R I0: amperes before first resistor I1=I0*5Ohm, Pmax=22 W ==> U^2/5Ohm=22W==>Umax=10.5 P2=U1^2/31.5=3.49W which is under the max of 10W P3=U2^2/15Ohm=0.81 which is under max of 10W So the greatest voltage is approximately 10.5 V b) R(total)=5+31.5+15=51.5Ohm P=10.5V^2/51.5Ohm=2.136 W

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