- Examples: 1. How much charge is represented by 4 ,600 electrons? 2. Calculate the amount of charge represented by two million protons. 3. The total charge entering a terminal is given by q=5tsin4pi tmC Calculate the current at t=0.5s 4. Determine the total charge entering a terminal between t=1s and t=2s if the current passing the terminal is i=(3t^2-t)A

1. The charge represented by 4,600 electrons can be calculated using the fundamental charge of an electron, which is approximately 1.6 x 10^-19 Coulombs. Therefore, the total charge is given by:<br /><br />Charge = Number of electrons x Charge of one electron<br /> = 4,600 x 1.6 x 10^-19 C<br /> = 7.36 x 10^-18 C<br /><br />2. The charge represented by two million protons can be calculated using the fundamental charge of a proton, which is approximately 1.6 x 10^-19 Coulombs. Therefore, the total charge is given by:<br /><br />Charge = Number of protons x Charge of one proton<br /> = 2,000,000 x 1.6 x 10^-19 C<br /> = 3.2 x 10^-12 C<br /><br />3. To calculate the current at t = 0.5s, we can use the formula for current, which is the rate of change of charge with respect to time. Given the equation for charge as q = 5t sin(4πt) mC, we can differentiate it with respect to time to get the current:<br /><br />Current = dQ/dt = 5(sin(4πt) + 4πt cos(4πt)) mA<br /><br />Substituting t = 0.5s into the equation, we get:<br /><br />Current = 5(sin(4π*0.5) + 4π*0.5 cos(4π*0.5)) mA<br /> = 5(0 + 2π) mA<br /> = 10π mA<br /><br />4. To determine the total charge entering a terminal between t = 1s and t = 2s, we need to integrate the current equation over this time interval. Given the equation for current as i = (3t^2 - t) A, we can integrate it with respect to time to get the charge:<br /><br />Charge = ∫(3t^2 - t) dt from 1s to 2s<br /><br />Integrating the equation, we get:<br /><br />Charge = [t^3 - (1/2)t^2] from 1s to 2s<br /> = [(2^3 - (1/2)*2^2) - (1^3 - (1/2)*1^2)] mC<br /> = (8 - 2) - (1 - 0.5) mC<br /> = 6 - 0.5 mC<br /> = 5.5 mC<br /><br />Therefore, the total charge entering the terminal between t = 1s and t = 2s is 5.5 mC.