$=0$ v$\_($S$)=$V$\_($SO$)$cos$(\backslash$omega t$)$

R$\_($S$)=400$ohm

V$\_($SO$)=580$mV

$\backslash$omega $=6\mathrm{.}28$k$($rad$)/(($s$))$

The temperature is monitored on a display $($the load$)$ with a vertical line of light$-$emitting diodes. Normal conditions are indicated when

a string of the bottommost diodes $2$ cm in length is on$.$

A voltage is supplied to the display input terminals where R$\_($L$)=12$ kohm, v$\_($O$)=$V$\_($m$)$cos$(\backslash$omega t$),$ and V$\_($m$)=6$V$.$

A voltage amplifier is connected between the sensor and CRT with R$\_($i$)=2$ kohm and R$\_($O$)=3$ kohm to amplify the sensor signal.

Determine the required no$-$load gain of the amplifier.

The required no$-$load gain of the amplifier is