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## Q. 5.8

Gyro Sensor

The purpose of the gyro is to detect and determine the orientation of an object to which it is attached. These systems have applications in self-localization such as Inertial Navigation Systems (INS), used in aeronautical systems, boats, etc. This allows a vehicle (mobile) to find its position at any time instance with respect to a bearing point Figure 5.24 (a) shows a gyro sensor while Figure 5.24 (b) shows a simplified circuit for a gyro sensor setup. In practice, a transistor is required in the circuit to maintain a minimum amount of current flow through the gyro’s sensor.

Use the simple equivalent circuit for the gyro shown in Figure 5.24 (b) to find the expression for the voltage across gyroscope, $v_R$.

## Verified Solution

Using the definition of $v_{C}(t)=V_{S}\left(1-e^{\frac{-t}{RC}}\right)$, obtain the expression for the voltage across the capacitor, which is:

$v_{C}(t)=5\left(1-e^{\frac{-t}{0.002475}}\right)$

Applying KVL, the expression for the voltage across the gyroscope, $V_{R}$, is:

$v_{R}(t)=V_{S}-v_{C}(t)$

Replacing for $v_{C}(t)$ :

$v_{R}(t)=e^{\frac{-t}{0.002475}}$

Notice that the voltage across the gyroscope drops to 0 V in a very short time period. In practice, a transistor is implemented to control and ensure a fixed amount of voltage and current flow through the gyroscope.