Devise the series or parallel combination of 2 capacitances from the
E6 series that gives the closest match to the capacitance 1.14 μF.
Indicate the percentage error between the desired value and the
value you obtain.
To find the series or parallel combination of capacitances from the E6 series that gives the closest match to the capacitance of 1.14 μF, we first need to understand the E6 series.
The E6 series is a standardized set of preferred values for resistors, capacitors, and other electronic components. The values in the E6 series increase logarithmically. For capacitors, the E6 series values are:
1.0, 1.5, 2.2, 3.3, 4.7, 6.8 (in microfarads)
To calculate the series combination, we add the values of the individual capacitances. For the parallel combination, we use the formula:
C_parallel = (C1 * C2) / (C1 + C2)
Let's find the closest match for the capacitance of 1.14 μF:
1. The closest match in the E6 series is 1.0 μF.
2. To find the percentage error, we use the formula:
Percentage error = |(desired value - obtained value) / desired value| * 100
In this case, the desired value is 1.14 μF, and the obtained value is 1.0 μF.
Percentage error = |(1.14 μF - 1.0 μF) / 1.14 μF| * 100
Calculating this, we get:
Percentage error = (0.14 μF / 1.14 μF) * 100
Percentage error ≈ 12.28%
Therefore, the series combination of two capacitances from the E6 series (1.0 μF and 0.0 μF) gives the closest match to the capacitance of 1.14 μF, with a percentage error of approximately 12.28%.