Question

In a radar system, peak transmitted power is increased a factor of $81$ and the antenna diameter is increased by a factor of $3$, then the maximum-range will increase by a factor of

• A. $81$
• B. $27$
• C. $9$
• D. $3$

Answer 1

The correct option is C $9$

$R_{max}\propto d\propto P^{\frac{1}{4}}$
$⟹\frac{R_2\left(newrange\right)}{R_1\left(originalrange\right)}=\frac{D_2\left(newdiameter\right)}{D_1\left(originaldiameter\right)}$
$=\frac{P_2^{\frac{1}{4}}\left(newtransmittedpower\right)}{P_1^{\frac{1}{4}}\left(originaltransmittedpower\right)}$
$=\frac{3D_1}{D_1}\times \frac{{\left(81P_1\right)}^{\frac{1}{4}}}{\frac{1}{4}}=3\times 3=9$