Two sources of equal E.M.F. are connected to external resistance R . The internal resistances of the two sources are R1 and R2 (R2 R1) . If the potential difference across the source having internal resistance R2 is zero, then

Question

Two sources of equal E.M.F. are connected to external resistance R . The internal resistances of the two sources are R1 and R2 (R2 > R1) . If the potential difference across the source having internal resistance R2 is zero, then (A) R=(R1 R2/R1 + R2) (B) R=(R1 R2/R2 - R1) (C) R=R2((R1 + R2)/(R2 - R1)) (D) R=R2-R1

Tardigrade Admin · Accepted Answer

Given, The potential difference across the cell is, E-IR2=0 Current flowing through the circuit is given by, I=(2 E/R1 + R2 + R) ∴ E=IR2 ⇒ E=(2 E R2/R1 + R2 + R) ⇒ R1+R2+R=2R2 ⇒ R=R2-R1

Q. Two sources of equal E.M.F. are connected to external resistance $R$ . The internal resistances of the two sources are $R_{1}$ and $R_{2}$ $(R_{2} > R_{1})$ . If the potential difference across the source having internal resistance $R_{2}$ is zero, then

$R = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$

$R = \frac{R _{1} R _{2}}{R _{2} - R _{1}}$

$R = R_{2} \frac{( R _{1} + R _{2} )}{( R _{2} - R _{1} )}$

$R = R_{2} - R_{1}$

Q. Two sources of equal E.M.F. are connected to external resistance R . The internal resistances of the two sources are R1​ and R2​ (R2​>R1​) . If the potential difference across the source having internal resistance R2​ is zero, then

R=R1​+R2​R1​R2​​

R=R2​−R1​R1​R2​​

R=R2​(R2​−R1​)(R1​+R2​)​

R=R2​−R1​

Given, The potential difference across the cell is, E−IR2​=0 Current flowing through the circuit is given by, I=R1​+R2​+R2E​ ∴ E=IR2​ ⇒E=R1​+R2​+R2ER2​​ ⇒R1​+R2​+R=2R2​ ⇒R=R2​−R1​

Q. Two sources of equal E.M.F. are connected to external resistance $R$ . The internal resistances of the two sources are $R_{1}$ and $R_{2}$ $(R_{2} > R_{1})$ . If the potential difference across the source having internal resistance $R_{2}$ is zero, then

$R = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$

$R = \frac{R _{1} R _{2}}{R _{2} - R _{1}}$

$R = R_{2} \frac{( R _{1} + R _{2} )}{( R _{2} - R _{1} )}$

$R = R_{2} - R_{1}$