Two Cells of Emfs 1.5 V and 2.0 V, Having Internal Resistances 0.2 Ω and 0.3 Ω, Respectively, Are Connected in Parallel. Calculate the Emf and Internal Resistance of the Equivalent Cell. - Physics


Two cells of emfs 1.5 V and 2.0 V,  having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.



E1=1.5 V

E2=2 V

r1=0.2 Ω

r2 =0.3 Ω

The effective emf of two cells connected in parallel can be calculated as follows: 

`E_(eff) = (E_1r_2+E_2r_1)/(r_1+r_2)`

`=> E_(eff) = (1.5xx0.3+2.0xx0.2)/0.5 = 1.7 V`

The effective resistance can be calculated as follows:

`R_(eff)= (r_1r_2)/(r_1+r_2)`

`=> R_(eff)= (0.2xx.03)/0.5`0.12 Ω

  Is there an error in this question or solution?
2015-2016 (March) Delhi Set 1

Video TutorialsVIEW ALL [1]


Distinguish between emf and terminal voltage of a cell.

A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being charged by a 120 V dc supply using a series resistor of 15.5 Ω. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the emf of the second cell?

A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.

The equivalent resistance between points. a and f of the network shown in Figure 2 is :

a) 24 Ω

b) 110 Ω

c) 140 Ω

d) 200 Ω

A resistor R is connected to a cell of-emf e and internal resistance r. The potential difference across the resistor R is found to be V. State the relation between e, V, Rand r.

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing the variation of terminal potential ‘V’ with resistance R. Predict from the graph the condition under which ‘V’ becomes equal to ‘E’.

Two non-ideal batteries are connected in series. Consider the following statements:-

(A) The equivalent emf is larger than either of the two emfs.

(B) The equivalent internal resistance is smaller than either of the two internal resistances.

Two non-ideal batteries are connected in parallel. Consider the following statements:-

(A) The equivalent emf is smaller than either of the two emfs.

(B) The equivalent internal resistance is smaller than either of the two internal resistances.

Find the value of i1/i2 in the following figure if (a) R = 0.1 Ω (b) R = 1 Ω and (c) R = 10 Ω. Note from your answers that in order to get more current from a combination of two batteries, they should be joined in parallel if the external resistance is small and in series if the external resistance is large, compared to the internal resistance.

Consider N = n1n2 identical cells, each of emf ε and internal resistance r. Suppose n1 cells are joined in series to form a line and n2 such lines are connected in parallel.

The combination drives a current in an external resistance R. (a) Find the current in the external resistance. (b) Assuming that n1 and n2 can be continuously varied, find the relation between n1, n2, R and r for which the current in R is maximum.

Find the equivalent resistance of the network shown in the figure between the points a and b.

How many time constants will elapse before the power delivered by a battery drops to half of its maximum value in an RC circuit?

Do all thermocouples have a neutral temperature?

Do the electrodes in an electrolytic cell have fixed polarity like a battery?

A coil of resistance 100 Ω is connected across a battery of emf 6.0 V. Assume that the heat developed in the coil is used to raise its temperature. If the heat capacity of the coil is 4.0 J K−1, how long will it take to raise the temperature of the coil by 15°C?

A plate of area 10 cm2 is to be electroplated with copper (density 9000 kg m−3) to a thickness of 10 micrometres on both sides, using a cell of 12 V. Calculate the energy spent by the cell in the process of deposition. If this energy is used to heat 100 g of water, calculate the rise in the temperature of the water. ECE of copper = 3 × 10−7 kg C−1and specific heat capacity of water = 4200 J kg−1.

Find the emf of the battery shown in the figure:

Two cells of emfs approximately 5 V and 10 V are to be accurately compared using a potentiometer of length 400 cm.

The internal resistance of dry cell is ...A..., than the internal resistance of common electrolytic cell. Here, A refers to ______.

A cell having an emf E and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by ______.

A straight line plot showing the terminal potential difference (V) of a cell as a function of current (I) drawn from it, is shown in the figure. The internal resistance of the cell would be then ______.

Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio `("R"/"r")` is:

The internal resistance of a cell is the resistance of ______

Two batteries of emf ε1 and ε22 > ε1) and internal resistances r1 and r2 respectively are connected in parallel as shown in figure.

A cell E1 of emf 6 V and internal resistance 2 Ω is connected with another cell E2 of emf 4 V and internal resistance 8 Ω (as shown in the figure). The potential difference across points X and Y is ______.

A battery of EMF 10V sets up a current of 1A when connected across a resistor of 8Ω. If the resistor is shunted by another 8Ω resistor, what would be the current in the circuit? (in A)

A block of metal is heated directly by dissipating power in the internal resistance of block. Because of temperature rise, the resistance increases exponentially with time and is given by R(t) = 0.5 e2t, where t is in second. The block is connected across a 110 V source and dissipates 7644 J heat energy over a certain period of time. This period of time is ______ × 10-1 sec (take ln 0.367 = -1).

An ac generator generates an emf which is given by e = 311 sin (240 πt) V. Calculate:

  1. frequency of the emf.
  2. r.m.s. value of the emf.


      Forgot password?
Use app×