Obtain the differential equations in the case of charging of capacitor in series L-C-R circuit?
Understand the Problem
The question is asking for the differential equations that describe the process of charging a capacitor in a series L-C-R circuit. This involves understanding the relationships between inductance (L), capacitance (C), resistance (R), and the voltage and current within the circuit.
Answer
L(d²Q/dt²) + R(dQ/dt) + (1/C)Q = E(t)
The differential equation for the charge Q(t) on the capacitor in a series L-C-R circuit is given by L(d²Q/dt²) + R(dQ/dt) + (1/C)Q = E(t), where L is the inductance, R is the resistance, C is the capacitance, and E(t) represents the external voltage source applied to the circuit.
Answer for screen readers
The differential equation for the charge Q(t) on the capacitor in a series L-C-R circuit is given by L(d²Q/dt²) + R(dQ/dt) + (1/C)Q = E(t), where L is the inductance, R is the resistance, C is the capacitance, and E(t) represents the external voltage source applied to the circuit.
More Information
This differential equation describes how the charge on a capacitor changes over time when in a circuit with an inductor and a resistor. It accounts for energy stored in the capacitor and inductor and lost or dissipated in the resistor.
Tips
A common mistake is neglecting the external voltage source term E(t) or incorrectly assigning the signs of the components, leading to incorrect formulation of the equation.
Sources
- Charging a Capacitor through Inductance and Resistance - LibreTexts - phys.libretexts.org
- Find the charge Q(t) on the capacitor in an L-R-C - Vaia - vaia.com
- The 'equation of motion' of a series LCR circuit - Chegg - chegg.com
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