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

RLC Circuit

Growth of cur...

Question

Growth of current in two different $L - R$ circuits are depicted by the $i - t$ graphs shown. Angle subtended by the curves with tine axis at time $t = 0$ are also shown in the graph. $τ_{1}$ and $τ_{2}$ are time constant for the circuits $1$ and $2$ respectively. Then the value of $\frac{τ_{1}}{τ_{2}}$ is

\frac{2}{3}

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

\frac{3}{2}

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

\frac{1}{2}

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

\frac{4}{1}

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

Open in App

Solution

The correct option is B $\frac{3}{2}$
$\begin{matrix} C i r c u i t 1 : i n i t i a l l y : E_{o} = \frac{L_{1} d i_{1}}{d t} = L_{1} [tan 30^{o}] = \frac{L_{1}}{\sqrt{3}} = L_{1} = \sqrt{3} E_{o} . . . . . . . . (1) f i n a l l y : i_{o} = \frac{E_{o}}{R_{1}} \Rightarrow R_{1} = \frac{E_{o}}{i_{o}} . . . . . . . (2) C i r c u i t 2 : i n i t i a l l y E_{o} = \frac{L_{2} d i_{2}}{d t} \Rightarrow E_{o} = L_{2} (tan 60^{o}) \Rightarrow L_{2} = \frac{E_{o}}{\sqrt{3}} . . . . . . . . . . (3) \Rightarrow R_{2} = \frac{E_{o}}{2 i_{o}} . . . . . . . . . . (4) ∴ r_{1} = \frac{L_{1}}{R_{1}} = \frac{\sqrt{3} E_{o} I_{o}}{E_{o}} = \sqrt{3} i_{o} r_{2} = \frac{L_{2}}{R_{2}} = \frac{E_{o} 2 i_{o}}{\sqrt{3} . E_{o}} = \frac{2 i_{o}}{\sqrt{3}} ∴ \frac{r_{1}}{r_{2}} = \frac{\sqrt{3} \times \sqrt{3}}{2} = \frac{3}{2} H e n c e, o p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

Suggest Corrections

Similar questions

Q. Two solid circular shafts of radii

R_{1}

and

R_{2}

are subjected to same torque. The maximum shear stesses developed in the two shafts are

τ_{1}

and

τ_{2}

. If

\frac{R_{1}}{R_{2}} = 2

, then

\frac{τ_{2}}{τ_{1}}

The charge flown through a circuit in the time interval between t and t+dt is given by $d q = e^{- t / τ} d t$ , where $τ$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $τ$

Q. A pure inductor, pure capacitor, and two pure equal resistors are connected as shown in the circuit, such that

L = 2 R^{2} C

.
At an instant

t = 0

, the switch is closed. If

i_{1}

and

i_{2}

are currents shown in branches at some time

t = t_{o}

relation

\frac{d i_{1}}{d t} + \frac{d i_{2}}{d t} = 0

is satisfied, then

Q. For given

L - R

circuit, growth of current as function of time

t

is shown in graph. Which of the following option represents value of time constant most closely for the circuit?

Q. Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from

τ_{1}

τ_{2}

. If

\frac{C_{p}}{C_{v}} = γ

for this gas then a good estimate for

\frac{τ_{2}}{τ_{1}}

is given by

Join BYJU'S Learning Program

Growth of current in two different L−R circuits are depicted by the i−t graphs shown. Angle subtended by the curves with tine axis at time t=0 are also shown in the graph. τ1 and τ2 are time constant for the circuits 1 and 2 respectively. Then the value of τ1τ2 is