Question

In the circuit shown the three ammeters (marked as 1, 2, 3) are identical, each have a resistance $R_{0} = 2 Ω$ . Between points $A$ and $B$ there is a constant potential difference of $19 V$ . The first and second ammeter read $I_{1} = 2.5 A$ and $I_{2} = 1.5 A$ , respectively.
(a) What is the reading of third ammeter?
(b) Calculate value of resistance $R$ .
(c) Investigate what happens to current $I_{3}$ if the value of $R_{x}$ is changed. Show approximately graphical variation of $I_{3}$ vs $R_{x}$ .

Note : Reading of ammeter implies current through branch of ammeter.

Accepted Answer

Writing the potential on every node will make the problem easy, as some currents are given.

Potential drop on ammeter $1$ is $I_{1} \times R_{0} = 2.5 \times 2 = 5 V$ , the potential at node $D$ will be $I_{2} = 1.5 A$

Potential drop on ammeter $2$ is $I_{2} \times R_{0} = 1.5 \times 2 = 3 V$ , the potential at node $C$ will be $16 V$

(a) The potential difference across third ammeter is $V_{C} - V_{D} = 16 - 14 = 2 V$ , therefore the current is

$I_{3} = \frac{V_{C} - V_{D}}{R_{0}} = \frac{2}{2} = 1 A$

(b) From figure the current through $R$ is $I_{1} + I_{3}$ and potential difference is $V_{D} - V_{B}$

Therefore, the values of $R$ is $R = (2.5 + 1) (14 - 0) = 49 Ω$

(c) The current through $R_{x}$ is $I_{3}$ , this indicates, if $R_{x}$ increases $I_{4}$ decreases and $I_{3}$ will increase, therefore on changing $R_{x}$ , $I_{3}$ changes accordingly.If $R_{x} \to \infty$ , $I_{3}$ will be maximum.

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