How do I combine three resistors which are in parallel with each other?

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The net resistance depends on the point where you have applied the potential difference. Indicating the direction of current is very useful.

You can Use $[$ $($ $R_3$ series $R_4$ $)$ parallel $R_2$ $]$ to be $R_7$

Now Redraw the circuit and by naming the point with same potential as one point as I have done in my diagram. Helps a lot:

Seems like I have made an error in direction of current in $R_7$ . It should be opposite. But it matters not as if you apply Kirchoff's law the current will come out to be negative.

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Updated on August 07, 2022

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  • user29157
    user29157 over 1 year

    For this circuit (a and b are connected by a battery),

    circuit diagram

    Will I be able to find the total resistance of the circuit by adding resistors that are in series and combining resistors that are in parallel without using the method of Kirchhoff's Voltage and Current Law?

    I tried adding R3+R4 and this forms one resistor, which is in parallel with R2 and R1. And R2 is in parallel with R1 and R3, and R1 is in parallel with R2 and R3. This can be verified by Kirchhoff's Voltage laws. The problem is, I get stuck here. I know that if R1,R2 and R3+R4 can be combined into one resistor, then parallel-series would solve the problem neatly. But I can't see how these resistors be combined.

    • Ross Millikan
      Ross Millikan almost 10 years
      Step by step: R3 and R4 are in series, so replace them with a single resistor R7. Now R2 and R7 are in parallel, then... You can get there this way
    • user29157
      user29157 almost 10 years
      @RossMillikan That's what I did, but then I get stuck.
    • user29157
      user29157 almost 10 years
      Can hold be released?
    • Ross Millikan
      Ross Millikan almost 10 years
      You can combine three parallel resistors just fine. One way is just to combine two of them (they are in parallel), then combine that with the third. Now you have one resistor in place of R1, R2, R3, R4.
    • user29157
      user29157 almost 10 years
      but then where would the combined resistor be? Would it be in series with R6? Or Would it be in series with R5?
    • Ross Millikan
      Ross Millikan almost 10 years
      Let R7 be the series combination of R3 and R4. It goes in place of them in the circuit. Then R8 is the parallel of R2 and R7 and goes in place of them in the circuit. Now combine R8 and R1 to make a single resistor R9 that takes their place. It is in series with R5 and the combo in parallel with R6
    • user29157
      user29157 almost 10 years
      But what would it mean that the combined resistor in series with R5 but also in parallel with R6? Drawing that, I really see no way to calculate the total resistance...
    • Ross Millikan
      Ross Millikan almost 10 years
      It is in series with R5, and the pair is in parallel with R6. So R10=R5+R9 and the circuit is the parallel of R6 and R10