Four resistances of 8, 8, 8 and 12 OHM form a Wheatstone network. What shunt is needed across the 12 OHM resistor to balance the network?

Question

Four resistances of 8, 8, 8 and 12 OHM form a Wheatstone network
What shunt is needed across the 12 OHM resistor to balance the
network?

Guru Prasad Singh · Accepted Answer

Let the resistance across 12 ohm be 'x'
Now , In balanced condition, 8/8=8/y=> y=8 ohm (say y
to be net resistance across 4th resistor
Now, According to condition,
1/x+1/12=1/y=> 12+x/12x= 1/8=> 96+8x=12x=>
4x=96=> x= 24 ohm
Hence the Shunt resistance to be connected across 12 ohm
resistance is 24 ohm
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