In the adjacent circuit find, (i) the current in resistor $R$, (ii) the unknown emf $E$, (iii) the resistance $R$, (iv) if the circuit is broken at $P$, what is the current in resistor $R$?

(i) Using Kirchhoff's current law at point $'D'$, 

Current through $R = 6 - 4 = 2\;A$ 

(ii) Applying Kirchhoff's voltage law in close loop ABCDA, 

$E = 3 \; *\; 6 \;+\; 4\; *\; 6 = 18\; + \;24 = 42\; V$ 

(iii) Again, Applying Kirchhoff's voltage law in close loop AFEDA, 

$E - 28 = 6 * 4 - R * 2$ 

$42 - 28 = 24 - 2R$ 

$2R = 24 - 14 = 10$

$R = 5 \; \Omega$

(iv) If the circuit is broken from point $'P'$ then,

Current$(I) = \frac{V}{R\; +\; 3} = \frac{28}{5\; + \;3}$   $= 3.5\; A$

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