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 $\left(\Omega \right)$	$V\left(Volt\right)$	$i(Amp.)$
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
• B. 8.1 W
• C. 8 W
• D. 7.9 W

Answer 1

The correct option is B 8.1 W

Let us draw thevenin equivalent of black box


$V_{TH}=i{R}_{TH}+V$ (applying KVL)
Using given data
$V_{TH}=1.5R_{TH}+3$ $...\left(i\right)$
$V_{TH}=1.0R_{TH}+8$ $...\left(ii\right)$
From (i) and (ii)
$V_{TH}=18V$
$R_{TH}=10\Omega$

Maximum power delivered, $=\frac{V_{TH}^2}{4R_{TH}}=\frac{{18}^2}{40}=8.1W$