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Answer (Detailed Solution Below)

Option 3 : $12\ \Omega$ / $12\ \Omega$

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Detailed Solution

सही उत्तर $12\ \Omega$ / $12\ \Omega$ है।

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Question:

In a Wheatstone bridge, the ratio arms are $P = 4\ \Omega$ and $Q = 6\ \Omega$, and the known arm is $R = 8\ \Omega$. For the bridge to be balanced, the unknown resistance $S$ must be: / व्हीटस्टोन सेतु में अनुपात भुजाएँ $P = 4\ \Omega$ और $Q = 6\ \Omega$ हैं, तथा ज्ञात भुजा $R = 8\ \Omega$ है। सेतु संतुलित होने के लिए अज्ञात प्रतिरोध $S$ होना चाहिए:

1.
$4\ \Omega$ / $4\ \Omega$
2.
$8\ \Omega$ / $8\ \Omega$
3.
$12\ \Omega$ / $12\ \Omega$
4.
$16\ \Omega$ / $16\ \Omega$

Correct Answer: $12\ \Omega$ / $12\ \Omega$

The balance condition is $P/Q = R/S$, so $S = QR/P = 6 \times 8 / 4 = 12\ \Omega$. / संतुलन शर्त $P/Q = R/S$ है, अतः $S = QR/P = 6 \times 8 / 4 = 12\ \Omega$।

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