Question

Three $10\Omega ,2W$ resistors are as in figure. The maximum possible voltage between points A and B without exceeding the power limits of any of the resistors is

• A. $5\sqrt{3}V$
• B. $3\sqrt{5}V$
• C. $15V$
• D. $\frac{5}{3}V$

Answer 1

Answer: (B)

$3\sqrt{5}V$

Power $=V^{2}R$

$V=\sqrt{PR}=\sqrt{2\times 10}=\sqrt{20}=2\sqrt{5}V$

Clearly, voltage across single resistor of $10$ ohm cannot exceed $2\sqrt{5}$V. Note that the resistance of parallel combination is half of $10$ ohm. Thus, the maximum possible voltage between A and B is $3\sqrt{5}V$.