SOLUTION: When two resistors S and T are connected in parallel their combined resistance R is given by the expression R=1/((1/S)+(1/T)) This expression can be rewritten as a ra

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Question 19411: When two resistors S and T are connected in parallel their combined resistance R is given by the expression
R=1/((1/S)+(1/T))

This expression can be rewritten as a rational expression in S and T. The numerator of that expression is ST and its denominator is S+T

Suppose you connect two resistors of the same resistance in parallel. Then the resistance of the two connected resistors equals _________ times that of each resistor alone.



Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
R=ST/(S+T)
Now if they have the same value,S=T
R=T*T(T+T)=(T^2/2T)
So the resistance would be (T^2/2T)


To find how many times it is greater than T alone,find the ratio:
Let the ratio be x
%28%28T%5E2%2F2T%29%29%2FT=x
%28T%5E2%2F2T%29%2A%281%2FT%29=x
%28T%5E2%2F2T%5E2%29=x
1%2F2=x
therefore our ratio is (1/2)


Thats your answer.
Hope this helps,
Prabhat