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Question

A black box with a circuit in it is connected to a variable resistor. An ideal ammeter and an ideal voltmeter are used to measure current and voltage as shown.

R (Ω) V(Volt) i(Amp.)
3 3 1.5
8 8 1.0
14 10.5 0.75

The maximum power that box can deliver is

A
8.5 W
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B
8.1 W
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C
8 W
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D
7.9 W
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Solution

The correct option is B 8.1 W
Let us draw thevenin equivalent of black box


VTH=iRTH+V (applying KVL)
Using given data
VTH=1.5RTH+3 ...(i)
VTH=1.0RTH+8 ...(ii)
From (i) and (ii)
VTH=18V
RTH=10Ω

Maximum power delivered, =V2TH4RTH=18240=8.1W




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