Advertisements
Advertisements
Question
Two cells of same emf E but internal resistance r1 and r2 are connected in series to an external resistor R (Figure). What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.
Advertisements
Solution
In this problem first we apply Ohm' law to find current in the circuit.
Effective emf of two cells = E + E = 2E
Effective resistance = R + r1 + r2
So the electric current is given by
`I = (E + E)/(R + r_1 + r_2)`
`V_1 = E - Ir_1 = E - (2E.r_1)/(R + r_1 + r_2)`
The net potential difference across 1st cell V1 = 0 (Given)
∴ `E - (2Er_1)/(R + r_1 + r_2)` = 0
Or `1 - (2r_1)/(R + r_1 + r_2)` = 0
`(2r_1)/(r_1 + r_2 + R) = 1/1`
Or 2r1 = r1 + r2 + R
| r1 – r2 = R |
It is the required condition for the potential difference across 1st cell to be zero.
APPEARS IN
RELATED QUESTIONS
Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?
Name the physical quantity whose unit is "ohm".
The graph between V and I for a conductor is a straight line passing through the origin.
- Which law is illustrated by such a graph?
- What should remain constant in a statement of this law?
How should the two resistances of 2 ohms each be connected so as to produce an equivalent resistance of 1 ohm?
What is an ohmic resistor? Give one example of an ohmic resistor. Draw a graph to show its current voltage relationship. How is the resistance of the resistor determined from this graph?
Show by a diagram how two resistors R1 and R2 are joined in parallel. Obtain an expression for the total resistance of the combination.
The filament of a bulb takes a current 100 mA when potential difference across it is 0.2 V. When the potential difference across it becomes 1.0 V, the current becomes 400 mA. Calculate the resistance of filament in each case and account for the difference.
Rewrite the following statement by selecting the correct option.
The S.I. unit of resistance is __________.
State the limitations of Ohm’s law.
Answer the following question.
Distinguish between Ohmic and non-ohmic substances; explain with the help of example.
Write a short note on superconductors?
Obtain the macroscopic form of Ohm’s law from its microscopic form and discuss its limitation.
Assertion: The statement of Ohm’s law is K = IR.
Reason: V = IR is the equation which defines resistance.
A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistances R1, R2 and R3 respectively. Which of the following is true?
The circuit depicted in the figure is employed for studying Ohm’s Law. Instead of using a standard resistor, a student opts for a glass tube filled with mercury (tube 1), connected to the circuit through two electrodes, E1 and E2. He records the readings of the ammeter and voltmeter, thereby calculating the resistance. The student repeats the experiment by substituting tube 1 with tube 2, where the same amount of mercury fills tube 2.
Neglecting internal resistance of the cell use (> or < or =) to compare:
- the resistance in both the cases.
- the voltmeter readings in both the cases.
- the specific resistance in both the cases.
When two conductors at different electric potentials are joined by a metallic wire, in which direction do the electrons flow?
A resistor is connected in a circuit with a voltage of 12 V and a resistance of 24 Ω. What is the current flowing through the resistor?
