Certain piezoelectric crystal having dimensions 6 mm - 6 mm - 1-5 mm is used for force measurement- The crytsal has voltage sensitivity constant of 50 - 10-3 V- m-N- A certain force produces an output voltage of 100 V across the crystal- If the charge sensitivity of the crytsal is 150PC-N then the developed charge is -

V_o = g.t.p = g.t FA ⇒ nbsp;F = A. V_og.t g = Voltage sensitivity = 50 × 10^ 3 Vm/N t =thickness = 1.5 mm = 1.5 × 10^ 3 m A = Area = 6× 6× 10^ 6m^2 V_o = ...

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Byju's Answer

Standard XII

Physics

Semiconductors and Superconductors

Certain piezo...

Question

Certain piezoelectric crystal having dimensions $6 m m \times 6 m m \times 1.5 m m$ is used for force measurement. The crytsal has voltage sensitivity constant of $50 \times 10^{- 3} V - m / N .$ A certain force produces an output voltage of 100 V across the crystal. If the charge sensitivity of the crytsal is 150PC/N then the developed charge is ?

7.2 PC

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7200 PC

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720 PC

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100 PC

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Solution

The correct option is B 7200 PC
$V_{o} = g . t . p = g . t \frac{F}{A}$

$\Rightarrow F = \frac{A . V_{o}}{g . t}$

$g = Voltage sensitivity = 50 \times 10^{- 3} V m / N$

$t = thickness = 1.5 m m = 1.5 \times 10^{- 3} m$

$A = Area = 6 \times 6 \times 10^{- 6} m^{2}$

$V_{o} = 100 V$

$F = \frac{36 \times 10^{- 6} \times 100}{50 \times 10^{- 3} \times 1.5 \times 10^{- 3}} = 48 N$

$Now charge sensitivity = \frac{Q}{F} = 150 P C / N$

$Q = 150 P C / N \times 48 N$

$Q = 7200 P C$

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The correct option is B 7200 PCVo=g.t.p=g.tFA ⇒F=A.Vog.t g=Voltage sensitivity=50×10−3Vm/N t=thickness=1.5mm=1.5×10−3m A=Area=6×6×10−6m2 Vo=100 V F=36×10−6×10050×10−3×1.5×10−3=48 N Now charge sensitivity=QF=150 PC/N Q=150PC/N×48N Q=7200 PC