Answer
423.6k+ views
Hint: At the time when the current starts flowing, we will have a minimum current at $t = 0$ .In this time the whole current will pass through resistance of $12\Omega $ and no current would be passing through inductors. After a long time, current will also pass through inductors, and we will have our maximum current.
Complete step by step answer:
At time $t = 0$, inductors will be acting as resistors of infinite resistance, so only current will be through the $12\Omega $ resistor. Hence it is ${I_{\min }}$.
At $t = 0$, circuit will be:
In reality, we don’t have resistances of infinite ohm with both inductors, but for visualization, both inductors will be acting as resistances of infinite ohm and there will be no current passing through them.
So using ohm’s law $V = {I_{\min }}R$, (where $V = 5$ volts and $R = 12\Omega $) we get,
${I_{\min }} = \dfrac{5}{{12}}Amp$
After a long time, inductors will not resist anymore, the only resistance will be due to their internal resistance and $12\Omega $ resistor.
After long time, equivalent circuit will be like this:
After a long time, resistance through inductors will only be due to their internal resistances and current will easily pass through them.
At that time, the equivalent resistance,
$\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{12}} + \dfrac{1}{3} + \dfrac{1}{4}$
On solving the above equation, we get,
$\Rightarrow$ $\dfrac{1}{{{R_{eq}}}} = \dfrac{{1 + 4 + 3}}{{12}}$
On solving this, we get equivalent resistance as,
$\Rightarrow$ $\dfrac{1}{{{R_{eq}}}} = \dfrac{8}{{12}} = \dfrac{3}{2}$
Now applying ohm’s law on $V = {I_{\max }}{R_{eq}}$, we get,
$\Rightarrow$ ${I_{\max }} = \dfrac{{5 \times 2}}{3}Amp = \dfrac{{10}}{3}Amp$
Required value $\dfrac{{{I_{\max }}}}{{{I_{\min }}}}$ will be,
$
\Rightarrow\dfrac{{{I_{\max }}}}{{{I_{\min }}}} = \dfrac{{10/3}}{{5/12}} \\
\Rightarrow\dfrac{{{I_{\max }}}}{{{I_{\min }}}} = \dfrac{{10 \times 12}}{{3 \times 5}} = 8 \\
$
So our answer is 8.
Note: At time $t = 0$, inductors will be acting as resistors of infinite resistance, so only current will be through $12\Omega $ resistor, which will give us minimum current. But after a long time, they will let the whole current pass through them and only resistance by them is due to their internal resistors and given resistance of $12\Omega $ and the current will be maximum.
Complete step by step answer:
At time $t = 0$, inductors will be acting as resistors of infinite resistance, so only current will be through the $12\Omega $ resistor. Hence it is ${I_{\min }}$.
At $t = 0$, circuit will be:
![seo images](https://www.vedantu.com/question-sets/a4039764-238e-4151-a383-004209952af05101128859263956717.png)
In reality, we don’t have resistances of infinite ohm with both inductors, but for visualization, both inductors will be acting as resistances of infinite ohm and there will be no current passing through them.
So using ohm’s law $V = {I_{\min }}R$, (where $V = 5$ volts and $R = 12\Omega $) we get,
${I_{\min }} = \dfrac{5}{{12}}Amp$
After a long time, inductors will not resist anymore, the only resistance will be due to their internal resistance and $12\Omega $ resistor.
After long time, equivalent circuit will be like this:
![seo images](https://www.vedantu.com/question-sets/81eabc5e-3d56-463a-aa43-540fd7672bc18262044244755845258.png)
After a long time, resistance through inductors will only be due to their internal resistances and current will easily pass through them.
At that time, the equivalent resistance,
$\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{12}} + \dfrac{1}{3} + \dfrac{1}{4}$
On solving the above equation, we get,
$\Rightarrow$ $\dfrac{1}{{{R_{eq}}}} = \dfrac{{1 + 4 + 3}}{{12}}$
On solving this, we get equivalent resistance as,
$\Rightarrow$ $\dfrac{1}{{{R_{eq}}}} = \dfrac{8}{{12}} = \dfrac{3}{2}$
Now applying ohm’s law on $V = {I_{\max }}{R_{eq}}$, we get,
$\Rightarrow$ ${I_{\max }} = \dfrac{{5 \times 2}}{3}Amp = \dfrac{{10}}{3}Amp$
Required value $\dfrac{{{I_{\max }}}}{{{I_{\min }}}}$ will be,
$
\Rightarrow\dfrac{{{I_{\max }}}}{{{I_{\min }}}} = \dfrac{{10/3}}{{5/12}} \\
\Rightarrow\dfrac{{{I_{\max }}}}{{{I_{\min }}}} = \dfrac{{10 \times 12}}{{3 \times 5}} = 8 \\
$
So our answer is 8.
Note: At time $t = 0$, inductors will be acting as resistors of infinite resistance, so only current will be through $12\Omega $ resistor, which will give us minimum current. But after a long time, they will let the whole current pass through them and only resistance by them is due to their internal resistors and given resistance of $12\Omega $ and the current will be maximum.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)