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53. Figure shows a circuit with known resistance R1 & R2. Neglect the internal resistance of the sources of the current and resistance of the connecting wire. The magnitude of electromotive force E1 such that the current through the resistance R is zero will be.

a )   E R 1 / R 2                                             B )     E R 2 / R 1                                     C )     E ( R 1 + R 2 ) R 2                           D )     E R 1 R 1 + R 2

Dear student

Let potential of negative terminal of the cell with emf E is zero   that is of point A is zero so potentia of different points are as VB=E    VC=E     Vd=-E1as there is no current in resistor across BE so potential of point B and E is same.VB=VC=EApplying Kirchoffs junction rule at the junction Cnet current diverging  from point E is zero.Current in CB+Current in CD+current in EF=00+E-(-E1)R1+E-0R2=0E+E1R1=-ER2R2(E+E1)=-E×R1ER2+E1R1=-E×R1E1R1=-E×R1-ER2E1=(-E×R1-ER2)R1=-E(R1+R2)R1magnitude of E1 isE1=E(R1+R2)R1Regards

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