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Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100 -pF capacitor through a $75.0-\mathrm{M} \Omega$ resistor to 90.0$\%$ of its final voltage.
.017 see
Physics 102 Electricity and Magnetism
Chapter 21
Circuits, Bioelectricity, and DC Instruments
Direct-Current Circuits
Hope College
University of Sheffield
University of Winnipeg
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so we will use the charging equation. We'II acquittal. We not which is E M f. Science one minus exponential negativity divided by tower. And we are given the potential difference or the capacitor is charged to 90% off the final voltage, which is reasonable. So this must be a 0.9 off the zero. The zero times one minus explanation. Negative to you, divided by top. So we can simply cancel the zero from both sides. Then one minus exponential tip divided. But how is equal to 0.9 So exponential negativity about it. My child is equal to 0.1. So let's take natural love on both side. This will yield negative. T by child is equal to natural log off 0.1, which is negative 2.3 zero to fight to six. Okay, so she is equal to negative 2.3026 sort of positive times toe. As we know, Tao is given by resistance times to capacitance. It's a 2.3023 times the resistance, which is 75 mega over 75 times 10 power six or multiplied by the capacitance of 100. Pico Fair which is 100 times 10 power. Negative. 12. So let's do that calculation. This will be 1 72 point seven times turn power Negative four, which is equal to 0.17 three seconds. So it will take 0.173 seconds to charge. Capacitor to point 0.9 and 90% of final vote. Oh, this is wrong. Here. This must be zero point 017 three as there is 10 power negative four. And this is Did you do your number? Thank you.
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