Advertisements
Advertisements
Question
Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in parallel across a resistor R.
Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential differences across the equivalent cell.
Advertisements
Solution
`R_{AB}` = ?
`1/(R_{AB}) = 1/(2r) + 1/(3r) + 1/(6r)`
`1/R_{AB} = 1/r[(3 + 2 + 1)/6]`
`1/R_{AB} = 1/r`
`R_{AB} = r` ⇒ equivalent internal resistant
Equivalent emf of cells in parallel,
`E_{eq} = (E_1/r_1 + E_2/r_2 + E_3/r_3)/(1/r_1 + 1/r_2 + 1/r_3)`
= `(E/(2r) + E/(3r) + E/(6r))/(1/(2r) + 1/(3r) + 1/(6r))`
`E_{eq} = E[(1/(2r) + 1/(3r) + 1/(6r))/(1/(2r) + 1/(3r) + 1/(6r))]`
Eeq = E
Current flowing in the circuit,
I = `E_{eq}/(R + R_{AB})`
I = `E/(R + r)`
Potential drop across E,
V = IReq
V = `(rE)/(R + r)`
APPEARS IN
RELATED QUESTIONS
A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.
It is found that when R = 4 Ω, the current is 1 A and when R is increased to 9 Ω, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.
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 secondary cell after long use has an emf of 1.9 V and a large internal resistance of 380 Ω. What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?
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.
A 10 V cell of negligible internal resistance is connected in parallel across a battery of emf 200 V and internal resistance 38 Ω as shown in the figure. Find the value of current in the circuit.
Plot a graph showing variation of voltage vs the current drawn from the cell. How can one get information from this plot about the emf of the cell and its internal resistance?
A cell of emf E and internal resistance r is connected to two external resistance R1 and R2 and a perfect ammeter. The current in the circuit is measured in four different situations:
(i) without any external resistance in the circuit
(ii) with resistance R1 only
(iii) with R1 and R2 in series combination
(iv) with R1 and R2 in parallel combination
The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in the order. Identify the currents corresponding to the four cases mentioned above.
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.
Internal resistance of a cell is the resistance offered by which component?
