10) Find the equivalent resistance across the nvo ends A and B of the following circuits
Answers
Given : identical resistors are joined in both circuit as shown in figure. R is the resistance of each resistor.
To find : The equivalent resistance across the two ends A and B of given circuits.
solution : (i) in this circuit, three resistors and two conducting wire are joined.
to find equivalent resistance, you should assume a single point of two points joining by conducting wire.
C and E are joined by conducting wire so, assume CE is a single point. similarly, DF is another single point.
now, effective resistance between A and B, Req :
see figure, all the three resistors are joined in parallel combination.
so, 1/Req = 1/R + 1/R + 1/R = 3/R
⇒Req = R/3
(ii) This is easily solved with help of Wheatstone bridge concept.
as it is balanced Wheatstone bridge so the current doesn't flow through PQ.
so, you can remove it from the circuit.
now equivalent Resistance between L and M :
1/R₁ = 1/(R + R) + 1/(R + R) = 2/2R = 1/R
so, R₁ = R
now R₁ and R are joined in parallel combination between A and B.
so, equivalent resistance, Req = R × R/(R + R) = R/2
Answer:
Explanation:
(i) in this circuit, three resistors and two conducting wire are joined.
to find equivalent resistance, you should assume a single point of two points joining by conducting wire.
C and E are joined by conducting wire so, assume CE is a single point. similarly, DF is another single point.
now, effective resistance between A and B, Req :
see figure, all the three resistors are joined in parallel combination.
so, 1/Req = 1/R + 1/R + 1/R = 3/R
⇒Req = R/3
(ii) This is easily solved with help of Wheatstone bridge concept.
as it is balanced Wheatstone bridge so the current doesn't flow through PQ.
so, you can remove it from the circuit.
now equivalent Resistance between L and M :
1/R₁ = 1/(R + R) + 1/(R + R) = 2/2R = 1/R
so, R₁ = R
now R₁ and R are joined in parallel combination between A and B.
so, equivalent resistance, Req = R × R/(R + R) = R/2