Question

For a tachometer, if $\theta \left(t\right)$ is the rotor displacement in radians, $e\left(t\right)$ is the output voltage and $K_t$ is the tachometer constant in $V/rad/sec$, then the transfer function,
$\frac{E\left(s\right)}{Q\left(s\right)}$ will be

• A. $K_t{s}^2$
• B. $\frac{K_t}{s}$
• C. $K_{t}s$
• D. $K_t$

Answer 1

The correct option is C $K_{t}s$



$\theta \left(t\right)=$ rotor displacement in radians
$\omega \left(t\right)=\frac{d\theta }{dt}=$ angular speed in $rad/sec$

Output voltage:
$e\left(t\right)=K_t\omega \left(t\right)=K_t\frac{d\theta }{dt}$

Taking Laplace transform on both sides

$E\left(s\right)=K_{t}s\theta \left(s\right)$

$\Rightarrow \frac{E\left(s\right)}{\theta \left(s\right)}=K_{t}s$