Physics

Physics

Problem

A biomedical sensor circuit must reach 63\% of its final charge in 2.0\,\text{s}. If the available resistor is 220\,k\Omega, what capacitance should be selected to meet this requirement? a) 2.3 μF2.3\,\mu\text{F} b) 440 μF440\,\mu\text{F} c) 9.0 μF9.0\,\mu\text{F} d) 13 μF13\,\mu\text{F}
Intuitive explanation

This is about the RC time constant and how it controls the charging speed of a capacitor. The key insight is that a capacitor reaches 63% of its final voltage in exactly one time constant τ=RC\tau = RC—this is a fundamental property of exponential charging. Since you know the time to reach 63% and the resistance, you can rearrange to find the capacitance that makes τ\tau equal to your required 2.0 s.

Intuitive explanation

This is about the RC time constant and how it controls the charging speed of a capacitor. The key insight is that a capacitor reaches 63% of its final voltage in exactly one time constant τ=RC\tau = RC—this is a fundamental property of exponential charging. Since you know the time to reach 63% and the resistance, you can rearrange to find the capacitance that makes τ\tau equal to your required 2.0 s.

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