Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are $R_{1}$ and $R_{2}$ ( $R_{2}$ > $R_{1}$ ). If the potential difference across the source having internal resistance R2 is zero, then what is the value of R?
OR
Two pure inductors, each of self-inductance L are connected in parallel but are well separated from each other, then what is the total inductance?
When the coils are connected in parallel, let the currents in the two coils be $i_{1}$ and $i_{2}$ respectively. Total induced current

Question

Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are $R_{1}$ and $R_{2}$ ( $R_{2}$ > $R_{1}$ ). If the potential difference across the source having internal resistance R2 is zero, then what is the value of R?
OR
Two pure inductors, each of self-inductance L are connected in parallel but are well separated from each other, then what is the total inductance?
When the coils are connected in parallel, let the currents in the two coils be $i_{1}$ and $i_{2}$ respectively. Total induced current

Accepted Answer

I=2εR+R1+R2Pot. difference across second cell=V=ε-IR2=0 ε=2εR+R1+R2.R2=0 R+R1+R2-2R2=0 R+R1+R2=0   ∴R=R2-R1 ORi=i1+i2 or didt=di1dt+di2dt               ……(1) Now e=L1di1dt=-L2di2dt (Q In parallel, induced e.m.f across each coil will be same) Hencedi1dt=-eL1 and di2dt=-eL2   ……(2) Let L' be the equivalent inductance. Then e=-L'didtordidt=-eL               ……(3) =cL'=-cL1-cL2or1L'=1L1+1L2 ∴L'=L1L2L1+L2 Here L1=L2=L ∴L'=L×LL+L=L2

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