Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Electric Current in a Charging R−C Circuit is Given by I = I0 E−T/Rc Where I0, R and C Are Constant Parameters of the Circuit and T is Time. - Physics

Sum

The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.

#### Solution

Given: i = i0 e−t/RC
∴ Rate of change of current
$= \frac{di}{dt}$
$= i_0 \left( \frac{- 1}{RC} \right) e^{- t/RC}$
$= \frac{- i_0}{RC} \times e^{- t/RC}$
On applying the conditions given in the questions, we get:
(a) At $t = 0, \frac{di}{dt} = \frac{- i_0}{RC} \times e^0 = \frac{- i_0}{RC}$
(b) At  $t = RC, \frac{di}{dt} = \frac{- i_0}{RC} \times e^{- 1} = \frac{- i_0}{RCe}$
(c) At $t = 10 RC, \frac{dt}{di} = \frac{- i_0}{RC} \times e^{10}$ $= \frac{- i_0}{RC e^{10}}$

Concept: What is Physics?
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 22 | Page 29
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