Answer:
Ratio of series current to parallel
= 1 : 8
Explanation:
Total resistance Rt
For series, Rt = 2+2+2+2 = 4ohms
For parallel, 1/Rt = 1/2 + 1/2 + 1/2 + 1/2
1/Rt = 4/2, Rt = 2/4 ohms.
If we use a 1V battery, then,
I = V/Rt
I = 1/4 = 0.25 ampere for series arrangement.
I = 1/0.5 = 2 ohms.
Ratio of current of series to parallel = 0.25 : 2
= 1 : 8
Resistance is the property of the conductor to lose some current in the form of heat. The ratio of electric current in series and the parallel connection is 1/8.
For series,
Rt = 2+2+2+2 = 4Ω
For parallel,
[tex]\dfrac 1{Rt} = \dfrac 12 + \dfrac 12 +\dfrac 12 + \dfrac 12 \\\\R_t = \dfrac 12[/tex]
The electric current in the wire,
[tex]I = \dfrac V{Rt}[/tex]
In series,
[tex]I_s= \dfrac {1}{4}\\\\I_s = 0.25[/tex]
In parallel,
[tex]I_p = \dfrac 1{\frac12}\\\\I_p = 2[/tex]
So, the ratio of the electric current is,
[tex]\dfrac {I_s}{I_p} = \dfrac {0.25}{2}\\\\\dfrac {I_s}{I_p} = \dfrac 18[/tex]
Therefore, the ratio of electric current in series and the parallel connection is 1/8.
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