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Exercise:
Calculate the possible resistances you can get by combining three resistors with resistances RaO RbO and RcO using one two or all three.

Solution:
Most combinations are straightforward: itemize item One resistor: Ra Rb Rc item Two resistors in series: itemize itemast Ra+RbRasbP itemast Rb+RcRbscP itemast Rc+RaRcsaP itemize item Two resistors in parallel: itemize itemast left/Ra+/Rbright^-RapbP itemast left/Rb+/Rcright^-RbpcP itemast left/Rc+/Raright^-RcpaP itemize item Three resistors in series: Ra+Rb+RcRabcsP item Three resistors in parallel: left/Ra+/Rb+/Rcright^-RabcpP itemize There are six more combinations with three resistors where either two resistors in series are in parallel to the third resistor or two resistors in parallel are in series to the third resistor see figure. center includegraphicswidthtextwidth#image_path:threresistors# center The resistance for the circuits in the first row can be calculated as follows: sscRtot RAabpcF With the different values for R_ R_ and R_ we get RAabpcP RAbcpaP and RAcapbP respectively. For the circuits in the second row the resitance can be calculated as follows: sscRtot RBasbcF The resulting resistances are RBasbcP RBbscaP and RBcsabP respectively.
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Exercise:
Calculate the possible resistances you can get by combining three resistors with resistances RaO RbO and RcO using one two or all three.

Solution:
Most combinations are straightforward: itemize item One resistor: Ra Rb Rc item Two resistors in series: itemize itemast Ra+RbRasbP itemast Rb+RcRbscP itemast Rc+RaRcsaP itemize item Two resistors in parallel: itemize itemast left/Ra+/Rbright^-RapbP itemast left/Rb+/Rcright^-RbpcP itemast left/Rc+/Raright^-RcpaP itemize item Three resistors in series: Ra+Rb+RcRabcsP item Three resistors in parallel: left/Ra+/Rb+/Rcright^-RabcpP itemize There are six more combinations with three resistors where either two resistors in series are in parallel to the third resistor or two resistors in parallel are in series to the third resistor see figure. center includegraphicswidthtextwidth#image_path:threresistors# center The resistance for the circuits in the first row can be calculated as follows: sscRtot RAabpcF With the different values for R_ R_ and R_ we get RAabpcP RAbcpaP and RAcapbP respectively. For the circuits in the second row the resitance can be calculated as follows: sscRtot RBasbcF The resulting resistances are RBasbcP RBbscaP and RBcsabP respectively.
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Attributes & Decorations
Branches
Direct Current
Tags
resistor, resistor circuit, series resistors
Content image
Difficulty
(1, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration