The internal resistance of a dry cell increases gradually with age, even though the cell is not used. The emf, however, remains fairly constant at 1.5 V. Dry cells must be tested for age at the time of purchase by connecting an ammeter directly across the terminals of the cell and reading the current. The resistance of ammeter is so small that the cell is practically short-circuited. (a) The short-circuit current of a fresh No. 6 dry cell (1.5 V, emf) is 25 A. What is the internal resistance? (b) What is the internal resistance if the short circuit current is only 10 A? (c) The short circuit current of a 6 V storage battery may be as great as 1000 A. What is its internal resistance?
ok..I am confused are we suppose to use the V=E-Ir? I don't know what equation to use!
Ohm's law can be stated as:
(resistance in ohms)= (voltage in volts)/(current in amps) .
For part (a):
resistance=(1.5V)/(25A)=0.06 ohms
Use the same equation for (b) and (c).
Well, let me help you out and try to shed some light on the situation. You're right, we can indeed use the equation V = E - Ir, where V is the terminal voltage, E is the emf, I is the current, and r is the internal resistance.
Let's tackle the problems one by one with a touch of humor:
a) To find the internal resistance of a fresh No. 6 dry cell, we need the short-circuit current. So, if a fresh No. 6 dry cell has a short-circuit current of 25 A, let's plug in the values into V = E - Ir. We know E is 1.5 V, and we're looking for r. Trying to isolate r, we can rearrange the equation to r = (E - V) / I. Substituting the values, we get r = (1.5 V - 0 V) / 25 A. Long story short, the internal resistance of the fresh cell is EEEEEEE-clear! (0.06 ohms)
b) Now, what if the short-circuit current is only 10 A? We can use the same equation, r = (E - V) / I. Plugging in the values again, we get r = (1.5 V - 0 V) / 10 A. The internal resistance of this cell is walking on thin wire—it’s 0.15 ohms!
c) Lastly, let's talk about the 6 V storage battery with a potentially booming short circuit current of 1000 A! Using our trusty equation once more, r = (E - V) / I, we find r = (6 V - 0 V) / 1000 A. Brace yourself for this shocker – the internal resistance of this battery is just a tiny spark—0.006 ohms!
Remember, these calculations are simplified, but hopefully, they put a smile on your face while dealing with internal resistances. If you have any more questions or need further assistance, I'm here to help, with a grin on my virtual face!
Yes, you are correct. In this case, you can use Ohm's Law, which states that V = E - IR, where V is the voltage across the terminals of the cell, E is the emf of the cell, I is the current flowing through the circuit, and R is the internal resistance of the cell.
Let's solve the questions step by step:
(a) To find the internal resistance of a No. 6 dry cell with a short-circuit current of 25 A and an emf of 1.5 V, we can rearrange Ohm's Law to solve for R.
V = E - IR
R = (E - V) / I
Substituting the given values:
R = (1.5 V - 0 V) / 25 A
R = 0.06 Ω
Therefore, the internal resistance of the fresh No. 6 dry cell is 0.06 Ω.
(b) For a short-circuit current of 10 A with the same emf of 1.5 V, we can use the same formula:
R = (1.5 V - 0 V) / 10 A
R = 0.15 Ω
Therefore, the internal resistance of the dry cell is 0.15 Ω.
(c) For a 6 V storage battery with a short-circuit current of 1000 A, we can again use Ohm's Law:
R = (6 V - 0 V) / 1000 A
R = 0.006 Ω
Therefore, the internal resistance of the 6 V storage battery is 0.006 Ω.
Yes, you are correct. In this case, you can use Ohm's Law, V = E - Ir, to calculate the internal resistance of the cell. In this equation, V represents the voltage across the terminals of the cell (which is equal to the emf, E), I represents the current flowing through the cell, and r represents the internal resistance of the cell.
Let's break down each part of the problem and solve it:
(a) First, we are given that the short-circuit current of a fresh No. 6 dry cell is 25 A and the emf is 1.5 V. The emf remains fairly constant, so we can use these values in the equation. Rearranging the equation to solve for r, we get r = (E - V) / I.
Substituting the given values, r = (1.5 V - 0 V) / 25 A = 0.06 Ω. Therefore, the internal resistance of a fresh No. 6 dry cell is 0.06 Ω.
(b) In this case, we are told that the short-circuit current is only 10 A, but the emf remains constant at 1.5 V. Using Ohm's Law, r = (1.5 V - 0 V) / 10 A = 0.15 Ω. Therefore, the internal resistance of the cell is 0.15 Ω when the short circuit current is 10 A.
(c) Lastly, we are given that the short circuit current of a 6 V storage battery can be as great as 1000 A. Using the same equation, r = (6 V - 0 V) / 1000 A = 0.006 Ω. Therefore, the internal resistance of the 6 V storage battery is 0.006 Ω.
Remember to always double-check your units and make sure they are consistent throughout the calculations.