(a)
Interpretation:
The function of the operational amplifier 1 should be determined.
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here, the given electronic circuit is as below:
Explanation of Solution
Given information:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below:
It can be seen that the operational amplifier 1 here performing the function of inverting voltage amplifier.
(b)
Interpretation:
The function of the operational amplifier 2 should be determined.
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below:
It can be seen that the operational amplifier 2 here performing the function of integrating circuit and hence the integration.
(c)
Interpretation:
The output voltage during the interval
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below:
Here the input voltage
Where
As per the problem switches
Here, the output signal can be given by the formula as below
Now assume
Substitute the values in the above equation and simplify, the result obtained is
The integrating voltage at different time intervals is given as:
Time(s) | Output Voltage (V) |
1 | 1 |
4 | 16 |
6 | 36 |
8 | 64 |
11 | 121 |
20 | 40 |
The plot can be obtained as shown below:
(d)
Interpretation:
The output voltage during the second interval
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Here the input voltage
Where
As per the problem switches
Here the output signal can be given by the formula as below
Where
Therefore, it can be said that
The output of the second operational amplifier which is actually the final output can be given by the equation as below:
Where
Now assume
Substitute the values in the above equation and simplify, the result obtained is
The integrating voltage at different time intervals is given as:
Time(s) | Output Voltage (V) |
1 | -1 |
4 | -16 |
6 | -36 |
8 | -64 |
11 | -121 |
20 | -40 |
The plot can be obtained as shown below:
(e)
Interpretation:
The output voltage
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Since there is no current so capacitor will discharge. And circuit will act as differentiator.
Further, it can be re-written as
The output can be given as
(f)
Interpretation:
The advantages and disadvantages of the given circuit over the normal amplifier should be described.
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Since there is no current so capacitor will discharge. And circuit will act as differentiator.
In general, the normal operational amplifier circuit can be used as a differentiator circuit only. But the given integrating circuit can be used as differentiator as well as integrator. Just one disadvantage is that the given circuit has higher noise level as compared to the normal circuit.
(g)
Interpretation:
The scenario if the input signal gets changes with the slope during the measurement cycle should be determined.
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Since there is no current so capacitor will discharge. And circuit will act as differentiator.
The output of the second operational amplifier which is actually the final output can be given by the equation as below:
Where
Now assume
Substitute the values in the above equation and simplify, the result obtained is
Further it can be written that
(h)
Interpretation:
The result obtained if the two-time intervals are separated by a time delay
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
For the given circuit the during the first time interval
Now if the two-time intervals are separated by a time delay
(i)
Interpretation:
The result if the two-time intervals were of different duration should be determined.
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
As its known that, if the two-time intervals are same then the plot of the output voltage is same in magnitude and opposite in sign for both the interval. But if the two-time intervals are of different duration then the magnitude of output signal will be different for both the time periods.
(j)
Interpretation:
The reason should be discussed for why the time interval is desirable to be as large as possible in measuring enzyme
Concept introduction:
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So, basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below:
Explanation of Solution
The operational amplifier is a high gain device and it amplifies the voltage. Generally, a voltage amplifier has a single output and differential input. So basically, an operational amplifier produces an output much higher than the input voltage. The output voltage could be thousands of times higher than the input voltage.
Here the given electronic circuit is as below
Since there is no current so capacitor will discharge. And circuit will act as differentiator.
The output of the second operational amplifier which is actually the final output can be given by the equation as below:
Where
Now, assume
Substitute the values in the above equation and simplify, the result obtained is
If the time gets larger then the output voltage also gets larger.
Enzyme kinematics are generally time-consuming process. So, its desirable to have larger time.
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Chapter 3 Solutions
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