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Series grouping

  • Same current flows through each resistance but potential difference distributes in the ratio of resistance, i.e., V R
    Fig. 13
  • Equivalent resistance is greater than the maximum value of resistance in the combination, i.e., Req = R1 + R2 + R3.
  • If n identical resistance are connected in series Req = nR and potential difference across each resistance V’ = V/n.

Parallel grouping

  • Same potential difference appeared across each resistance but current distributes in the reverse ratio of their resistance, i.e., i ∝ 1/R.
    Fig. 14
  • Equivalent resistance is given by
    or 70649.png
    Equivalent resistance is smaller than the minimum value of resistance in the combination.
  • If two resistances in parallel,
  • Current through any resistance,
    where i’ = required current (branch current), i = main current 70678.png and 70684.png
    Fig. 15
  • In n identical resistance are connected in parallel Req = R/n and current through each resistance i’ = i/n.
  • If n identical resistances are first connected in series and then in parallel, the ratio of the equivalent resistance is given by 72165.png.
  • If equivalent resistance of R1 and R2 in series and parallel be Rs and Rp, respectively, then
    72171.png and 72289.png
    If a wire of resistance R is cut in n equal parts and then these parts are collected to form a bundle, then equivalent resistance of combination will be R/n2.

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