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Step 5Parallel resistance - How to
Study the example in this photo until you understand it thoroughly. Remember what was said about BRANCHES in step 4.
TIP: A quick way to find the sum of two parallel resistances is to divide their product by their sum:
Rt=(R1xR2)/(R1+R2).
If R1=20 and R2=30, then Rt=20x30/20+30=600/50=12
It follows that if R1=R2, then Rt= half of one of them.
If R1=20 and R2=20, then Rt=20x20/20+20=400/40=10
::: In the example below, think of 't' as TOP, 'v' as VERTICAL, and 'b' as BOTTOM.
::: BRANCH 3 consists of Rt3, Rv3, and Rb3 in SERIES. Therefore Rs3=Rt3+Rv3+Rb3=30+40+50=120 by our SERIES Rule. Rs3 is now in PARALLEL with Rv2 and the EQUIVALENT resistance, Req1, is calculated as described under TIP, above:
Req1=(Rs3xRv2)/(Rs3+Rv2)= (120x30)/(120+30)=3600/150=24
Now BRANCH 3 has an equivalent resistance of 24
::: BRANCH 2 consists of Rt2, Req1 and Rb2 in SERIES. Therefore Rs2=Req1+Rt2+Rb2=24+40+20=84 by our SERIES Rule. Rs2 is now in PARALLEL with Rv1 and the EQUIVALENT resistance, Req2, is calculated as described in TIP, above:
Req2=(Rs2xRv1)/(Rs2+Rv1)=(84x40)/(84+40)=3360/124=27
Now BRANCH 2 has an EQUIVALENT resistance of 27
::: BRANCH 1 consists of Rt1, Req2 and Rb1 in SERIES. Therefore Req3, now Rt= Req2+Rt1+Rb1=27+10+50=87, the TOTAL RESISTANCE of the circuit. VOILA !
TIP: A quick way to find the sum of two parallel resistances is to divide their product by their sum:
Rt=(R1xR2)/(R1+R2).
If R1=20 and R2=30, then Rt=20x30/20+30=600/50=12
It follows that if R1=R2, then Rt= half of one of them.
If R1=20 and R2=20, then Rt=20x20/20+20=400/40=10
::: In the example below, think of 't' as TOP, 'v' as VERTICAL, and 'b' as BOTTOM.
::: BRANCH 3 consists of Rt3, Rv3, and Rb3 in SERIES. Therefore Rs3=Rt3+Rv3+Rb3=30+40+50=120 by our SERIES Rule. Rs3 is now in PARALLEL with Rv2 and the EQUIVALENT resistance, Req1, is calculated as described under TIP, above:
Req1=(Rs3xRv2)/(Rs3+Rv2)= (120x30)/(120+30)=3600/150=24
Now BRANCH 3 has an equivalent resistance of 24
::: BRANCH 2 consists of Rt2, Req1 and Rb2 in SERIES. Therefore Rs2=Req1+Rt2+Rb2=24+40+20=84 by our SERIES Rule. Rs2 is now in PARALLEL with Rv1 and the EQUIVALENT resistance, Req2, is calculated as described in TIP, above:
Req2=(Rs2xRv1)/(Rs2+Rv1)=(84x40)/(84+40)=3360/124=27
Now BRANCH 2 has an EQUIVALENT resistance of 27
::: BRANCH 1 consists of Rt1, Req2 and Rb1 in SERIES. Therefore Req3, now Rt= Req2+Rt1+Rb1=27+10+50=87, the TOTAL RESISTANCE of the circuit. VOILA !
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