Question 14.1: An amplifier has a voltage gain of 10, an input resistance o......
An amplifier has a voltage gain of 10, an input resistance of 1 kΩ and an output resistance of 10 Ω. The amplifier is connected to a sensor that produces a voltage of 2 V and has an output resistance of 100 Ω, and to a load resistance of 50 Ω. What will be the output voltage of the amplifier (that is, the voltage across the load resistance)?
Step-by-Step
First, we draw an equivalent circuit of the amplifier, sensor and load.
The input voltage is applied across a potential divider formed by R_{s} and R_{i} . The resulting voltage V_{i} is given by
V_{i} = \frac{R_{i}}{R_{s} + R_{i}} V_{s} = \frac {1 kΩ}{100 Ω + 1 kΩ} 2 V = 1.82 VThis voltage is amplified by the voltage source and the resultant voltage is applied across a second potential divider formed by R_{o} and R_{L} . Therefore, the output voltage is given by
V_{0} = A_{v} V_{i} \frac{R_{L}}{R_{0} + R_{L}} = 10 V_{i} \frac {50 Ω}{10 Ω + 50 Ω} = 10 × 1.82 \frac {50 Ω}{10 Ω + 50 Ω} = 15.2 V
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