JEE MAIN - Physics (2019 - 11th January Morning Slot - No. 5)
In a Wheatstone bridge(see fig.), Resistances P and Q are approximately equal. When R = 400 $$\Omega $$, the bridge
is balanced. On interchanging P and Q, the value of R, for balance, is 405 $$\Omega $$. The value of X is close to :
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402.5 ohm
401.5 ohm
403.5 ohm
404.5 ohm
Explanation
For a balanced bridge,
$${P \over Q} = {{400} \over X}$$ ......(i)
After interchanging P and Q,
$${Q \over P} = {{405} \over X}$$ ......(ii)
Multiplying equation (i) and (ii), we get
X2 = 400$$ \times $$405
$$ \Rightarrow $$ X = $$\sqrt {400 \times 405} $$ = 402.5 $$\Omega $$
$${P \over Q} = {{400} \over X}$$ ......(i)
After interchanging P and Q,
$${Q \over P} = {{405} \over X}$$ ......(ii)
Multiplying equation (i) and (ii), we get
X2 = 400$$ \times $$405
$$ \Rightarrow $$ X = $$\sqrt {400 \times 405} $$ = 402.5 $$\Omega $$
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