A capacitor with a capacitance of 10 µF is charged to a voltage of 100 V. What is the energy stored in the capacitor?
["# Energy Stored in a 10 µF Capacitor Charged to 100 V: A Complete Calculation", "When working with capacitors in electrical circuits, understanding how much energy is stored is essential for designing and analyzing systems. In this article, we’ll explore the calculation of energy stored in a 10 µF (microfarad) capacitor charged to a voltage of 100 volts (V) — a common scenario in basic electronics and physics applications.", "## What is a Capacitor?", "A capacitor is an electronic component that stores electrical energy in an electric field between two conductive plates separated by a dielectric material. Its ability to store charge is measured in farads (F), where 1 F means one coulomb of charge stored at one volt.", "## The Energy Stored in a Capacitor", "The energy ( E ) stored in a capacitor is given by the formula:", "[\nE = \frac{1}{2} C V^2\n]", "Where:\n- ( E ) = energy in joules (J)\n- ( C ) = capacitance in farads (F)\n- ( V ) = voltage across the capacitor in volts (V)", "This formula comes from integrating the energy contributed by the incremental charge ( dq ) as the capacitor charges from 0 to ( V ), using ( q = CV ) and ( dq = C,dV ).", "## Plugging in the Values", "For our capacitor:\n- Capacitance ( C = 10 , \mu\ ext{F} = 10 \ imes 10^{-6} , \ ext{F} )\n- Voltage ( V = 100 , \ ext{V} )", "Substitute into the energy formula:", "[\nE = \frac{1}{2} \ imes (10 \ imes 10^{-6} , \ ext{F}) \ imes (100 , \ ext{V})^2\n]", "First compute ( V^2 ):", "[\n100^2 = 10,000 , \ ext{V}^2\n]", "Now compute the full expression:", "[\nE = \frac{1}{2} \ imes 10 \ imes 10^{-6} \ imes 10,000 = 0.5 \ imes 0.1 = 0.05 , \ ext{J}\n]", "## Result: Energy Stored is 0.05 Joules", "Thus, a 10 µF capacitor charged to 100 V stores exactly 0.05 joules (50 millijoules) of energy.", "## Why This Matters", "Understanding stored energy in capacitors is critical for applications such as:\n- Flash photography and pulse circuits\n- Power backup and filtering in power supplies\n- Timing circuits and resonance applications", "The energy stored depends quadratically on voltage, meaning small voltage increases significantly increase stored energy — a key safety and design consideration.", "## Summary", "- Capacitance ( C = 10 , \mu\ ext{F} = 10^{-5} , \ ext{F} )\n- Voltage ( V = 100 , \ ext{V} )\n- Energy ( E = \frac{1}{2} C V^2 = 0.05 , \ ext{J} )", "Knowing how to compute this helps engineers and electronics enthusiasts accurately assess capacitor performance and safety in real-world systems.", "---", "**Keywords: capacitor energy storage, 10 µF capacitor, 100 V capacitor, how much energy in a capacitor, capacitor formula E = ½CV², electrical energy calculation."]
