You visited us 1 times! Enjoying our articles? Unlock Full Access!

Mixed Combination of Cells

Two cells wit...

Question

Two cells with the same emf $E$ and different internal resistances $r_{1}$ and $r_{2}$ are connected in series to an external resistance $R$ . The value of $R$ so that the potential difference across the first cell be zero, is

\sqrt{r_{1} r_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{1} + r_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{1} - r_{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{r_{1} + r_{2}}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $r_{1} - r_{2}$
The two cells have potential $E$ each and respective internal resistance $r_{1}$ and $r_{2}$ .
Let the current flowing in the circuit be $i$ .

Using Kirchhoff's voltage law:
$\Rightarrow - E + i r_{1} + i R - E + i r_{2} = 0$
$\Rightarrow i = \frac{2 E}{(R + r_{1} + r_{2})}$

Potential across first cell, $V_{A B} = i r_{1} - E = \frac{2 E r_{1}}{(R + r_{1} + r_{2})} - E$

For $V_{A B} = 0$ , we get: $\frac{2 E r_{1}}{(R + r_{1} + r_{2})} - E = 0$

$\Rightarrow$ $\frac{2 r_{1}}{(R + r_{1} + r_{2})} = 1$

$\Rightarrow 2 r_{1} = R + r_{1} + r_{2}$

$\Rightarrow R = r_{1} - r_{2}$

Suggest Corrections

Similar questions

Two cells with the same emf E and different internal resistance $r_{1} a n d r_{2}$ , are connected in series to an external resistance R. The value of R so that the pd across the ﬁrst cell is zero, is:

Q. Two cells of same emf

E

but different internal resistances

r_{1}

and

r_{2}

are connected in series with an external resistance

R

. The potential drop across the first cell is zero. Then

R

Q. Two cells having the same emf are connected in series through an external resistance

R

. Cells have internal resistances

r_{1}

and

r_{2}

such that

r_{1} > r_{2}

respectively. When the circuit is closed, the potential difference across the first cell is zero, then the value of

R

Q. Two cells of same emf are in series with an external resistance R. The internal resistance

r_{1}

r_{2}

. The p.d across the

1^{s t}

cell is found to be zero the value of R is

Q. Two cells, having the same e.m.f are connected in series through an external resistance R. Cells have internal resistance

r_{1}

and

r_{2}

(

r_{1}

r_{2}

) respectively. When the circuit is closed, the potential difference across the first cell is zero. the value of R is

Join BYJU'S Learning Program

Two cells with the same emf E and different internal resistances r1 and r2 are connected in series to an external resistance R. The value of R so that the potential difference across the first cell be zero, is

Two cells with the same emf $E$ and different internal resistances $r_{1}$ and $r_{2}$ are connected in series to an external resistance $R$ . The value of $R$ so that the potential difference across the first cell be zero, is