Tricky “Current" Current!!!
There is only a resistor of unknown resistance in a circuit. Then a 12ohm resistor is connected to the circuit such that the ratio of the Previous Current and Current Current, Ip:Ic=3:5 .
Then just simply find out the equivalent resistance of the current circuit( in ohm).
The answer is 4.8.
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1 solution
Its clearly seen that the current increased as we connected the 12 Ω resistor.
So it must've been connected in "Parallel" combination.
To explain more mathematically, as Ip:Ic=3:5; which is less than 1, so the resistor was connected in parallel.
Now assume,
Voltage=V
Resistance of the first resistor =R1
Previous current =Ip
Current current =Ic
Given that,
Ip/Ic=3:5
Resistance of the second resistor,R2=12 Ω
Equivalent resistance of the previous circuit= R1
So Previous Current, Ip= V/R1
Equivalent resistance of the current circuit=1/(1/R1+1/R2)=(R1R2)/(R1+R2)
So Current Current, Ic=V/{(R1R2)/(R1+R2)}
So, Ip/Ic=(V/R1)/[V/{(R1R2)/(R1+R2)}=3/5
or, {(R1R2)/(R1+R2)}/R1=3/5
or, R2/(R1+R2)=3/5
or, 3R1+3R2=5R2
or, R1=2R2/3
Putting the value of R2, we get,
R1=(24/3) Ω=8 Ω
Finally, equivalent resistance of the current circuit =(R1R2)/(R1+R2)=(96/20) Ω= 4.8 Ω
So the answer is 4.8 Ω.
Here, the clue to solve this is the “Current Current"!!!