Question

Two coils have self-inductance L1 = 4 mH and L2= 1 mH respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If I1 and l2 are the currents in the two coils at that instant of time respectively, then the value of $\frac { \mathrm { I } _ { 1 } } { \mathrm { I } _ { 2 } }$ is

• A. $\frac { 1 } { 8 }$
• B. $\frac { 1 } { 4 }$
• C. $\frac { 1 } { 2 }$
• D. 1

Answer 1

Answer: (B)

$\frac { 1 } { 4 }$

Answer 2

$| \varepsilon | = \mathrm { L } \frac { \mathrm { dI } } { \mathrm { dt } }$

$\mathrm { L } = \frac { | \varepsilon | } { \mathrm { dI } / \mathrm { dt } } = \frac { \mathrm { IR } } { \mathrm { dI } / \mathrm { dt } } = \frac { \mathrm { IP } / \mathrm { I } ^ { 2 } } { \mathrm { dI } / \mathrm { dt } } = \frac { \mathrm { P } } { 1 ( \mathrm { dI } / \mathrm { dt } ) }$

As P and (dI/dt) are same for both the coils