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Suppose a circuit contains an electromotive force (a battery) that produces a voltage of E(t) volts (V), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (2). The voltage drop across the capacitor is where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives Q = E(t). C RI + dQ we have dt 1 Since I = OP GQ = E(t). dt Suppose the resistance is 102, the capacitance is 0.1F, a battery gives a constant voltage of 40V, and the initial charge is Q(0) = 0 coulombs. Find the charge and the current at time t. Q(t) = I(t) =

Suppose a circuit contains an electromotive force (a battery) that produces a voltage of E(t) volts (V), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (2). The voltage drop across the capacitor is where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives Q = E(t). C RI + dQ we have dt 1 Since I = OP GQ = E(t). dt Suppose the resistance is 102, the capacitance is 0.1F, a battery gives a constant voltage of 40V, and the initial charge is Q(0) = 0 coulombs. Find the charge and the current at time t. Q(t) = I(t) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose a circuit contains an electromotive force (a battery) that produces a voltage of E(t) volts (V), a capacitor with a capacitance of farads (F), and a resistor with a resistance of R ohms (2). The voltage drop across the capacitor is Q where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives Q * = E(t). RI + C dQ we have dt Since I dQ R- Q = E(t). + dt Suppose the resistance is 102, the capacitance is 0.1F, a battery gives a constant voltage of 40V, and the initial charge is Q(0) = 0 coulombs. Find the charge and the current at time t. Q(t) = I(t) ||
Transcribed Image Text:Suppose a circuit contains an electromotive force (a battery) that produces a voltage of E(t) volts (V), a capacitor with a capacitance of farads (F), and a resistor with a resistance of R ohms (2). The voltage drop across the capacitor is Q where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives Q * = E(t). RI + C dQ we have dt Since I dQ R- Q = E(t). + dt Suppose the resistance is 102, the capacitance is 0.1F, a battery gives a constant voltage of 40V, and the initial charge is Q(0) = 0 coulombs. Find the charge and the current at time t. Q(t) = I(t) ||
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