Home
Class 12
PHYSICS
In the figure both cells A and B are of ...

In the figure both cells A and B are of equal emf. Find R for which potential difference across battery A will be zero, long time after the switch is closed. Internal resistance of batteries A and B `(r_1) and (r_2)` respectively`(r_(1)gtr_(2))`.

Text Solution

Verified by Experts

After a long time, steady state is reached in which impendance due to inductor `(omegaL` for `dc`) is zero and that due to capcitance
`((1)/(omega C))` becomes infinite, so equivalent circuit is shows in Fig
Net external resistance `R_(ext) = ((R )/(2) + R)/(2) = (3)/(4) R`
Net internal resistance `R_("int") = r_(1) + r_(2)`
`:.` Current in circuit `I = (2E)/((3)/(4) R + r_(1) + r_(2))`

The potential difference across the terminals of cell `A` is zero, so
`E - Ir_(1) = 0 rArr E - (2Er_(1))/((3)/(4) R + r_(1) + r_(2)) rArr R = (4)/(3) (r_(1) - r_(2))`.
Promotional Banner

Topper's Solved these Questions

  • INDUCTANCE

    CENGAGE PHYSICS|Exercise Solved Examples|3 Videos

  • INDUCTANCE

    CENGAGE PHYSICS|Exercise Exercise 4.1|24 Videos

  • HEATING EFFECT OF CURRENT

    CENGAGE PHYSICS|Exercise Thermal Power in Resistance Connected in Circuit|28 Videos

  • KINETIC THEORY

    CENGAGE PHYSICS|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

In a network as shown in the figure the potential difference across the resistance 2R is (the cell has an emf of E and has no internal resistance):

The figure shows a network in which the cell is deal and it has an emf E. The potential difference across the resistance 2R is

Internal resistance of battery of emf 2E is R_1 and battery of emf E is R_2 . If the potential difference across the cell of emf 2E is zero, then value of R is

In the circuit shown in figure E_1=10 V, E_2=4V, r_1=r_2=1Omega and R=2Omega . Find the potential difference across battery 1 and battery 2.

If E is the emf of a cell of internal resistance r and external resistance R, then potential difference across R is given as

Under what condition, the current passing through the resistance R can be increased by short - circuiting the battery of emf E_2 The internal resistances of the two batteries are r_1 and r_2, respectively.

In the given circuit, if the potential difference across the internal resistance r_1 is equal to E, then the resistance R is equal to:

Two sources of emf 6 V and internal resistance 3 Omega and 2 Omega are connected to anexternal resistance R as shown. If potential difference across battery A is zero, then the value of R is

In the circuit cell are of equal emf E but of difference internal resistance r_(1) = 6 Omega reading of the ideal voltmeter connected across cell 1 is zero The value of the external resistance R is ohm is equal to

Two cells of emf E each and internal resistance r_(1) and r_(2) are connected in series across a load resistance R. If potential difference across the first cell is zero, then find the relation between R, r_(1) and r_(2)