Calculate the effective wavelength in a slotline-waveguide.
Using the formula:
\[
\lambda_{slot} = \frac{c}{f\sqrt{\epsilon_{\text{eff}}}}
\]
where \( c \approx 3 \times 10^8 \) m/s.
* Enter the operating frequency (Hz) and the effective relative permittivity.
Example: \(1 \times 10^9\) Hz (1 GHz)
Example: 1 for air
Calculate the horsepower of a DC motor.
Using the formula:
\[
HP = \frac{V \times I \times \eta}{746}
\]
where \( \eta \) is the efficiency (entered as a percentage and converted to a decimal).
* Enter the motor voltage (V), current (A), and efficiency (%).
Example: 120 V
Example: 10 A
Example: 90% (Enter 90 for 90%)
Calculate the RMS thermal noise voltage using:
\[
V_n = \sqrt{4\,k\,T\,R\,B}
\]
* Enter temperature (K), resistance (Ω), and bandwidth (Hz).
Example: 300 K (approximately room temperature)
Example: 100 Ω
Example: 1000 Hz
Calculate the resistivity of a wire using:
\[
\rho = \frac{R \times A}{L}
\]
* Enter the measured resistance (Ω), wire length (m), and cross-sectional area (m²).
Example: 10 Ω
Example: 100 m
Example: 1e-6 m² (for a 1 mm² wire, convert mm² to m²)
For an inverting op-amp, the output voltage is given by:
\[
V_{out} = -\left(\frac{R_f}{R_{in}}\right)V_{in}
\]
To achieve a desired gain magnitude \(|A_v|\), use:
\[
|A_v| = \frac{R_f}{R_{in}} \quad \Rightarrow \quad R_f = |A_v| \times R_{in}
\]
* Enter the desired gain (magnitude) and the value of \(R_{in}\) (in ohms).
Example: 10 (for a gain of -10)
Example: 1000 Ω (1 kΩ)
Calculate the effective Geometric Mean Radius (GMR) of bundled conductors.
For a 2-conductor bundle: \[ \text{GMR} = \sqrt{r \times D} \] For a 3-conductor bundle (equilateral triangle): \[ \text{GMR} = \left(r \times D^2\right)^{\frac{1}{3}} \]
Example: 0.01 m (1 cm)
For 2-conductor: center-to-center distance; for 3-conductor (equilateral), spacing between any two conductors.
Example: 100 m
Calculate the RMS (effective) value of a sine wave.
Using the formula:
\[
V_{rms} = \frac{V_m}{\sqrt{2}}
\]
where \(V_m\) is the peak voltage.
Example: 170 V
Calculate the effective turns ratio of an ideal transformer.
Using the formula:
\[
a = \frac{N_p}{N_s}
\]
Example: 100 turns
Example: 50 turns
Calculate the total inductance of a double-circuit transmission line using the formula:
\[
L’ = \frac{\mu_0}{\pi}\ln\left(\frac{D_{eq}}{r}\right)
\]
and
\[
L_{\text{total}} = L’ \times L
\]
with \(\mu_0 = 4\pi \times 10^{-7}\, \text{H/m}\).
* Enter the effective spacing, conductor radius, and line length.
Enter the effective center-to-center spacing between circuits (e.g., 1 m)
Enter the radius of the conductor (e.g., 0.01 m)
Total length of the transmission line (e.g., 100 m)
For air, use 1; for other media, use the appropriate value.
Calculate the average DC output voltage of a full-wave rectifier.
Using the formula:
\[
V_{DC} = \frac{2\,V_m}{\pi}
\]
where \(V_m\) is the peak AC voltage.
Example: 170 V (peak voltage for a 120 V RMS supply)
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