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In the circuit given in the figure, the power consumed in the resistance R is measured when one source is acting at a time, these values are 18 W, 50 W and 98 W. When all the sources are acting simultaneously, possible maximum and minimum values of power in R will be
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- 98 W and 18 W
- 166 W and 18 W
- 450 W and 2 W
- 166 W and 2 W
Correct Option: C
| P1 = 18 = | ||
| R |
| P2 = 50 = | ||
| R |
| P3 = 98 = | ||
| R |
| Maximum power, Pmax = | ||
| R |
| = | ||
| R |
⇒ Pmax = P1 + P2 + P3 + 2(√P1P2 + √P2P3 + √P3P1)
= 18 + 50 + 98 + 2 √18 × 50 + 2 √50 × 98 + 2 √18 × 98 = 450 watts
| Minimum power, Pmax = | ||
| R |
= P1 + P2 + P3 - 2√P1P3 - 2√P2P3 + 2√P1P2)
= 18 + 50 + 98 - 2 √18 × 98 - 2 √50 × 98 + 2 √18 × 50 = 2 watts
