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21. Current in a Circuit When the circuit in Figure 6 (which consists of a battery of V volts, a resistor of R ohms, and an inductor of L henries) is connected, the current I (t) flowing in the circuit satisfies dI L + RI = V dt with the initial condition I (0) = 0. (a) Find a formula for I (t) in terms of L, V, and R. (b) Show that lim I(t) = V/R. (c) Show that I (t) reaches approximately 63% of its maximum value at the "characteristic time" t = L/R. Inductor Battery Resistor FIGURE 6 Current flow approaches the level Imax = V/R.

21. Current in a Circuit When the circuit in Figure 6 (which consists of a battery of V volts, a resistor of R ohms, and an inductor of L henries) is connected, the current I (t) flowing in the circuit satisfies dI L + RI = V dt with the initial condition I (0) = 0. (a) Find a formula for I (t) in terms of L, V, and R. (b) Show that lim I(t) = V/R. (c) Show that I (t) reaches approximately 63% of its maximum value at the "characteristic time" t = L/R. Inductor Battery Resistor FIGURE 6 Current flow approaches the level Imax = V/R.

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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21. Current in a Circuit When the circuit in Figure 6 (which consists of a battery of V volts, a resistor of R ohms, and an inductor of L henries) is connected, the current I (t) flowing in the circuit satisfies dI L + RI = V dt with the initial condition I (0) = 0. (a) Find a formula for I (t) in terms of L, V, and R. (b) Show that lim I(t) = V/R. (c) Show that I (t) reaches approximately 63% of its maximum value at the "characteristic time" t = L/R.
Transcribed Image Text:21. Current in a Circuit When the circuit in Figure 6 (which consists of a battery of V volts, a resistor of R ohms, and an inductor of L henries) is connected, the current I (t) flowing in the circuit satisfies dI L + RI = V dt with the initial condition I (0) = 0. (a) Find a formula for I (t) in terms of L, V, and R. (b) Show that lim I(t) = V/R. (c) Show that I (t) reaches approximately 63% of its maximum value at the "characteristic time" t = L/R.
Inductor Battery Resistor FIGURE 6 Current flow approaches the level Imax = V/R.
Transcribed Image Text:Inductor Battery Resistor FIGURE 6 Current flow approaches the level Imax = V/R.
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