GATE 2015 EC – Question 50

Analog Circuits · Op-amp Circuits · 2 marks · Numerical answer

In the circuit shown, assume that the opamp is ideal. The bridge output voltage $V_0$ (in mV) for $\delta = 0.05$ is ________.

A bridge made of resistors $250(1 + \delta)\ \Omega$, $250(1 - \delta)\ \Omega$, $250(1 - \delta)\ \Omega$ and $250(1 + \delta)\ \Omega$ is driven by an op-amp circuit with 1 V at the non-inverting input and $100\ \Omega$ resistors in series with the bridge, returning to a $50\ \Omega$ resistor to ground.

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Correct answer: 249 to 251

Explanation

The op-amp forces 1 V across the $50\ \Omega$ resistor, so the current is $\frac{1}{50} = 20$ mA. This current flows through the bridge. Each bridge arm pair has $250(1 + \delta) + 250(1 - \delta) = 500\ \Omega$, so the two arms in parallel are $250\ \Omega$, and the voltage across the bridge is $20\ \text{mA} \times 250 = 5$ V. The bridge output is $V_0 = 5 \times \delta = 0.25$ V, which is 250 mV.