# Problem: At what time has the current in the 8 Ω resistor decayed to half the value it had immediately after the switch was closed?

###### FREE Expert Solution

Equivalent resistance for 2 resistors in parallel:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

For 2 capacitors in series, the equivalent capacitance is::

$\overline{){{\mathbf{C}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}\frac{{\mathbf{C}}_{\mathbf{1}}{\mathbf{C}}_{\mathbf{2}}}{{\mathbf{C}}_{\mathbf{1}}\mathbf{+}{\mathbf{C}}_{\mathbf{2}}}}$

For capacitors in parallel, the equivalent capacitance is:

$\overline{){{\mathbf{C}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}{{\mathbf{C}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{C}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{C}}}_{{\mathbf{n}}}}$

The decay equation for current:

$\overline{)\begin{array}{rcl}{\mathbf{i}}& {\mathbf{=}}& {\mathbf{i}}_{\mathbf{0}}{\mathbf{e}}^{\mathbf{-}\mathbf{t}}{\mathbf{R}\mathbf{C}}}\end{array}}$

The equivalent resistance:

Req = 8 + (30)(20)/(30 + 20) = 20Ω

88% (71 ratings)
###### Problem Details

At what time has the current in the 8 Ω resistor decayed to half the value it had immediately after the switch was closed?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the !! Resistor-Capacitor Circuits concept. If you need more !! Resistor-Capacitor Circuits practice, you can also practice !! Resistor-Capacitor Circuits practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Batell's class at PITT.