The figure below shows three identical resistors with R = 125 connected between

Question

The figure below shows three identical resistors with R = 125 connected between terminals a and b. Each resistor can safely withstand a maximum power of16.0 W.

(a) What is the upper limit on the safe voltage that can be applied across the terminals?

(b) How much power is delivered to each of the three resistors at the maximum voltage found in part (a)?

(c) How much total power is delivered to the combination of three resistors?
W

Explanation / Answer

a)
For parallel resistors, R' = 125/2 = 62.5 ohm
P=V^2/R'
16 = V^2 / 62.5
V= 31.6 V
this is safe voltage across parallel resistors

for other resistor:
P=V^2/R
16 = V^2 / 125
V= 44.7 V
this is safe voltage across other resistor

So total safe voltage be Vsafe such that voltage across parallel combination shouldn't crosss 31.6 V and across other resistor shouldn't cross 44.7 V

By voltage division rule, voltage across parallel combination will be 1/2 of voltage across single resistor

so, 44.7 V is our main concern

SO,
Vsafe = 44.7 + (44.7/2) = 67.05 V

b)
V across top and bottom resistor = 44.7/2=22.35 V
P of topmost = V^2/R = 22.35^2/125= 4 W
P of bottom = V^2/R = 22.35^2/125= 4 W
V across right resistor = 44.7 V
P of right = V^2/R = 44.7^2/125= 16 W

c)
Total power = 4+4+16 = 24 w

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