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Series connection of parallel resistors:
A series-parallel circuit is formed by connecting a set of parallel resistors in series.
  1. Connect \(R_1\) and \(R_2\) in parallel to obtain an effective resistance of \(R_{P1}\).
  2. Similarly, connect \(R_3\) and \(R_4\) in parallel to get an effective resistance of \(R_{P2}\).
  3. These parallel segments of resistors are then joined in series.
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Series-parallel combination of resistors
 
The formula for the effective resistance of the parallel combination of resistors is
 
1RP=1R1+1R2+1R3
 
For two resistors in the circuit, the effective resistance is given as
 
1RP1=1R1+1R21RP2=1R1+1R2
 
Using the effective resistance of the series circuit, RS=R1+R2+R3, the net effective resistance of the series-parallel combination of resistors is,
 
RTotal=RP1+RP2
Parallel connection of series resistors:
A parallel-series circuit is formed by connecting a set of series resistors in parallel.
  1. Connect \(R_1\) and \(R_2\) in series to get an effective resistance of \(R_{S1}\).
  2. Similarly, connect \(R_3\) and \(R_4\) in series to get an effective resistance of \(R_{S2}\).
  3. These series segments of resistors are then joined in parallel.
6.png
Parallel-series combination of resistors
 
Using the effective resistance of the series circuit, RS=R1+R2+R3, we get
 
RS1=R1+R2RS2=R3+R4
 
Using the formula for the effective resistance of the parallel combination of resistors 1RP=1R1+1R2+1R3, the net effective resistance of parallel-series combination of resistors is
 
1RTotal=1RS1+1RS2.