A constant voltage V 0 ( = 12 V ) is applied to a potential divider of resistance R ( = 4Ω ) , connected to an ideal ammeter. A constant resistor r ( = 2Ω ) is connected to the sliding contact of th

Question

A constant voltage V 0 ​ ( = 12 V ) is applied to a potential divider of resistance R ( = 4Ω ) , connected to an ideal ammeter. A constant resistor r ( = 2Ω ) is connected to the sliding contact of the potential divider (as shown). Find the minimum current (in A ) measured by ammeter.

TestHub · Accepted Answer

Let x be the resistance between a & b then, x ∥ r . The totla resistance of circuit = r + x r x ​ + ( R − x ) So, current through ammeter I A ​ = r + x I 0 ​ r ​ = rx + ( R − x ) ( r + x ) V 0 ​ r ​ for its minimum value, ( dx dI A ​ ​ ) = 0 ⇒ we get x = 2 R ​ So, ( I A ​ ) m i n ​ = R ( r + 4 R ​ ) V 0 ​ r ​ = 4 ( 2 + 1 ) ( 12 ) ( 2 ) ​ = 2 A

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