(A)The total resistance of the parallel resistors is: [tex]R_{T} = \frac{R_{1} \times R_{2} \times R_{3}}{R_{2}R_{3}+R_{1}R_{3}+R_{1}R_{2}}[/tex]
(B) The current in the overall circuit is: [tex]I_{T} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}[/tex]
(C) The current through each resistance is as follows:
For the three resistances connected in parallel, R1, R2, R3 , the total resistance, [tex]R_{T}[/tex] is calculated as follows:
[tex]R_{T} = \frac{R_{1} \times R_{2} \times R_{3}}{R_{2}R_{3}+R_{1}R_{3}+R_{1}R_{2}}[/tex]
The current in the overall circuit is calculated using the formula:
[tex]I_{T} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}[/tex]
The current through each resistance is given as follows;
Current through R1, [tex]I_{1} = \frac{V}{R_{1}}[/tex]
Current through R2; [tex]I_{2} = \frac{V}{R_{2}}[/tex]
Current through R3; [tex]I_{3} = \frac{V}{R_{3}}[/tex]
In conclusion, the voltage across resistances in parallel is the same but the current varies.
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