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Question: In the Wheatstone's bridge shown it current \[2A\] enters at A, then what is the value of current in...

In the Wheatstone's bridge shown it current 2A2A enters at A, then what is the value of current in arm BC?

Explanation

Solution

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by adjusting two legs of an extension circuit, one leg of which incorporates the unknown segment. The essential advantage of the circuit is its capability to give amazingly accurate estimations

Formula used:
PQ=RS\dfrac{P}{Q} = \dfrac{R}{S}
Where, P,Q,RP, Q, R and SS are electrical resistances.
Ohm’s law: V=IRV = IR

Complete step by step answer:
It is given that a current of 2A2A is passing through the vertex A. Let the current flowing through the arm ABC be IAmperesI\,Amperes.The current flowing through the arm ADC will be the remaining left from the value of 2A2A.The current flowing through the arm ADC be (2I)Amperes\left( {2 - I} \right)\,Amperes.Since the voltage flowing through the circuit is unknown, we can take it as VV.

The net resistance in arm ABC will be RABC=10+5=15{R_{ABC}} = 10 + 5 = 15
The net resistance in arm ADC will be RADC=30+15=45{R_{ADC}} = 30 + 15 = 45
We know that ohm’s law gives us the relation between current, resistance and voltage.
V=15IV = 15I
V=45(2I)=9045I\Rightarrow V = 45(2 - I) = 90 - 45I
The voltage through arms ABC and ADC are the same, so we arrive at the equation:
Equating these two equations against each other, we have

\Rightarrow (45 + 15)I = 90 $$ In order to find the value of current flowing through arm ABC, we have to isolate the variables and the constants, that gives us: $$\therefore I = \dfrac{{90}}{{60}} = 1.5A$$ **Therefore, the current flowing through arm ABC is $$1.5\,A$$.** **Note:** In wheatstone bridge, under balanced conditions no current flows from the galvanometer. The galvanometer is a device that detects the presence of current. It also measures the very low or feeble current flowing through the circuit. The essential advantage of the circuit is its capability to give amazingly accurate estimations.