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Question
Four resistances 6Ω, 6Ω, 6Ω and 18Ω form a Wheatstone bridge. Find the resistance which connected across the 18Ω resistance will balance the network.
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Solution
Given: P = Q = R = 6 Ω
To find: Resistance (X)
Formula: `"P"/"Q" = "R"/"S"`
Calculation:
Let resistance connected across 18 Ω be X.
Equivalent resistance for 18 Ω and X in parallel is given by,
X' = S = `(18"X")/(18 + "X")`
From formula,
`6/6 = 6/((18"X")/(18 + "X"))`
∴ 1 = `(6(18 + "X"))/(18"X")`
∴ 18X = 108 + 6X
∴ 12X = 108
∴ X = 9 Ω
The resistance connected across 18 Ω resistance to balance the network is 9 Ω.
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