We would like to use the relation V (t) = I (t) RV (t) = I (t) R to find the voltage and current in the circuit as functions of time. To do so, we use the fact that current can be expressed in terms of the voltage. This will produce a differential equation relating the voltage V (t) V (t) V (t) to its derivative. Rewrite the right-hand side of this relation, replacing I (t) I (t) I (t) with an expression involving the time derivative of the voltage. Express your answer in terms of dV (t) / dt dV) / dt dV (t) / dt and quantities given in the problem introduction.

Question

Mathematics

Jennifer

24 August, 07:23

We would like to use the relation V (t) = I (t) RV (t) = I (t) R to find the voltage and current in the circuit as functions of time. To do so, we use the fact that current can be expressed in terms of the voltage. This will produce a differential equation relating the voltage V (t) V (t) V (t) to its derivative. Rewrite the right-hand side of this relation, replacing I (t) I (t) I (t) with an expression involving the time derivative of the voltage. Express your answer in terms of dV (t) / dt dV) / dt dV (t) / dt and quantities given in the problem introduction.

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Answers (1)

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Lorelai Hahn · Answer 1

Step-by-step explanation:

Given that

V (t) = I (t) R

Differentiating both sides with respect to t

dV (t) / dt=RdI (t) / dt

Divide both side by R

Therefore,

dI (t) / dt=1/RdV (t) / dt