Bot GPT 4-o mini To solve the problem, we first need to understand that the bridge configuration mentioned (likely a Wheatstone bridge) produces an output voltage that is sensitive to changes in resistance.
When the bridge is balanced, the output voltage \( V_{out} \) is zero. The balance of a Wheatstone bridge can be expressed using the resistances in the four arms of the bridge:
- Let the resistances be:
- \( R_1 = R_2 = R_3 = R_4 = 400 , \Omega \) (initially)
As the force increases, one of the resistances will change. In this case, the resistance of the strain gauge increases to:
- \( R_4 = 409 , \Omega \) (the strain gauge)
Bridge Output Calculation
In a Wheatstone bridge, the output voltage \( V_{out} \) can be calculated using the formula:
\[ V_{out} = V_s \cdot \frac{(R_2 / (R_2 + R_1)) - (R_4 / (R_3 + R_4))}{1} \]
Where:
- \( V_s \) is the supply voltage (15V in this case)
- \( R_1 = 400 , \Omega \)
- \( R_2 = 400 , \Omega \)
- \( R_3 = 400 , \Omega \)
- \( R_4 = 409 , \Omega \)
Plugging in the values
Using the input values:
-
For the left side of the bridge: \[ \frac{R_2}{R_1 + R_2} = \frac{400}{400 + 400} = \frac{400}{800} = 0.5 \]
-
For the right side of the bridge: \[ \frac{R_4}{R_3 + R_4} = \frac{409}{400 + 409} = \frac{409}{809} \approx 0.506 \]
Now calculate \( V_{out} \)
Now substituting these values back into the output voltage formula:
\[ V_{out} = 15V \left( 0.5 - 0.506 \right) = 15V \cdot (-0.006) \approx -0.09V \]
Thus, the voltage output \( V_{out} \) when the force exerts 200N and changes the resistance of the strain gauge to 409 Ohms is approximately -0.09V.
This indicates that the output is negative, which means the voltage would be measured below the reference point (0V).
1 answer