## Electrical Engineering: Principles & Applications (6th Edition)

Published by Prentice Hall

# Chapter 1 - 1.2 - Problems - Circuits, Currents, and Voltages: P1.12

#### Answer

The charge that passes through between 0 and 10 milliseconds is: 0 Coulombs The charge that passes through between 0 and 15 milliseconds is: 15.9 mC

#### Work Step by Step

We know the following equation for charge: $Q = \int_{t_0}^{t} idt$ Using substitution, we obtain: $Q = \int_{0}^{.01} 5sin(200 \pi t)dt \\ Q = 0$ We now solve for the charge from 0 to 15 milliseconds using the same process: $Q = \int_{0}^{.015} 5sin(200 \pi t)dt$ Using a calculator to evaluate this integral, we find: $Q = 15.9\ mC$

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