Advertisements
Advertisements
प्रश्न
Two cells of emf E1, E2 and internal resistance r1 and r2 respectively are connected in parallel as shown in the figure.
Deduce the expressions for
(1) the equivalent e.m.f of the combination
(2) the equivalent resistance of the combination, and
(3) the potential difference between the point A and B.
Advertisements
उत्तर
Let I1 and I2 be the current in two cells with emf E1 and E2 and internal resistance r1 and r2
So I = I1 + I2
Now let V be the potential difference between the points A and B. Since the first cell is connected between the points A and B.
V = potential difference across first cell
V = E1 − I1r1
`or I_1 =(E_1-V)/r_1`
Now, the second cell is also connected between the points A and B. So,
`or I_2 =(E_2-V)/r_2`
Thus, substituting for I1 and I2
`I =(E_1-V)/r_1 + (E_2-V)/r_2`
`or, I (E_1 /r_1 + E_2 /r_2)-V(1 /r_1 +1 /r_2)`
`V =((E_1r_2 + E_2r_1)/(r_1+r_2)) -I((r_1r_2)/(r_1 +r_2)) ..... (1)`
If E is effective e.m.f and r, the effective internal resistance of the parallel combination of the two cells then V = E − Ir …..(2)
Comparing (1) and (2)
`(1) E= (E_1r_2 + E_2r_1)/(r_1+r_2)`
This is equivalent e.m.f of the combination
`(2)r =(r_1r_2)/(r_1 +r_2)`
This is equivalent resistance of the combination.
(3) The potential difference between the point A and B is
V = E − Ir
संबंधित प्रश्न
A battery of emf 12 V and internal resistance 2 Ω is connected to a 4 Ω resistor as shown in the figure.
(a) Show that a voltmeter when placed across the cell and across the resistor, in turn, gives the same reading.
(b) To record the voltage and the current in the circuit, why is voltmeter placed in parallel and ammeter in series in the circuit?
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
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 battery of emf 100 V and a resistor of resistance 10 kΩ are joined in series. This system is used as a source to supply current to an external resistance R. If R is not greater than 100 Ω, the current through it is constant up to two significant digits.
Find its value. This is the basic principle of a constant-current source.
Find the equivalent resistance of the network shown in the figure between the points a and b.
Do the electrodes in an electrolytic cell have fixed polarity like a battery?
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 ______.
If n cells each of emf e and internal resistance r are connected in parallel, then the total emf and internal resistance will be ______.
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).
A cell of emf E is connected across an external resistance R. When current 'I' is drawn from the cell, the potential difference across the electrodes of the cell drops to V. The internal resistance 'r' of the cell is ______.
