Engineering

How do I calculate the correct resistor for an LED circuit?

Use Ohm's law: R = (V_supply − V_LED) / I_LED. For a typical red LED (V_LED ≈ 2V, I_LED ≈ 20mA) on a 5V supply: R = (5 − 2) / 0.02 = 150Ω. Also check power rating: P = I²R = 0.02² × 150 = 0.06W, so a standard ¼W resistor is sufficient. Our Ohm's law calculator automates these computations.

What is the formula for gear ratio and mechanical advantage?

Gear ratio = Number of teeth on driven gear ÷ Number of teeth on driver gear. A ratio > 1 means speed reduction with torque multiplication; a ratio < 1 means speed increase with torque reduction. For compound gear trains, multiply individual stage ratios. Mechanical advantage in ideal gears equals the gear ratio (neglecting friction losses).

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Beam deflection depends on load type, support conditions, material stiffness (Young's modulus E), and cross-section geometry (moment of inertia I). For a simply supported beam with center load: δ = PL³/(48EI). For a cantilever with end load: δ = PL³/(3EI). Our beam calculator handles multiple load and support configurations using Euler-Bernoulli beam theory.

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In parallel, capacitances add: C_total = C₁ + C₂ + ... (like resistors in series). In series, reciprocals add: 1/C_total = 1/C₁ + 1/C₂ + ... (like resistors in parallel). This is because parallel capacitors increase effective plate area, while series capacitors increase effective plate separation. Our capacitor calculator handles both configurations.

Are these engineering calculators suitable for professional design work?

Our calculators implement standard engineering formulas and are suitable for preliminary design estimates, educational purposes, and quick verification checks. However, professional engineering design requires compliance with specific codes (NEC, ASME, Eurocode), safety factors, environmental conditions, and professional engineering judgment. Always validate critical designs with licensed professional engineers and code-compliant analysis tools.