The series combination of two batteries, both of the same emf $$10$$ V, but different internal resistance of $$20$$Ω and $$5$$Ω , is connected to the parallel combination of two resistors $$30$$Ω and xΩ . The voltage difference across the battery of internal resistance $$20$$Ω is zero, the value of $$x(in$$ Ω $$)$$ is $$------$$

Question

The series combination of two batteries, both of the same emf $$10$$ V, but different internal resistance of $$20$$Ω   and $$5$$Ω  , is connected to the parallel combination of two resistors $$30$$Ω and xΩ . The voltage difference across the battery of internal resistance $$20$$Ω   is zero, the value of $$x(in$$ Ω $$)$$ is $$------$$

Infinity Learn · Accepted Answer

For first battery, $$V1=$$ε$$1$$−i.$$r1$$         ​⇒$$0=10$$−i×$$20$$  ∵$$V1=0$$         ​⇒ $$i=0.5A$$    For second battery , $$V2=$$ε$$2$$−$$ir2=10$$−$$0.5$$×$$5$$​⇒$$V2=7.5V$$            ​As per Kirchhoffs rule​  $$i=i1+i2$$                ​⇒ $$0.5=7.530+7.5x$$    ​⇒$$0.5=0.25+7.5x$$ ⇒$$7.5x=0.25$$​⇒$$x=30$$

Kirchoff's Law

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Kirchoff's Law

Remember concepts with our Masterclasses.

For first battery, V1=ε1−i.r1 ​⇒0=10−i×20 ∵V1=0 ​⇒ i=0.5A For second battery , V2=ε2−ir2=10−0.5×5​⇒V2=7.5V ​As per Kirchhoffs rule​ i=i1+i2 ​⇒ 0.5=7.530+7.5x ​⇒0.5=0.25+7.5x ⇒7.5x=0.25​⇒x=30

Ready to Test Your Skills?

free study material