A battery has an unknown e.m.f, ε,and an internal resistance r = 0.40Ω. When a resistance R = 5.60Ω is connected across the terminals of the battery, the terminal potential difference across the battery is 11.2V. What is the e.m.f. of the battery?
Hey , try yourself this time and Henry or I or someone will check.
I = V/R = 11.2/5.6 = 2A.
e.m.f. = I * (r+R) = 2 * (0.4+5.6) =
To find the e.m.f. of the battery, we can use the formula:
V = ε - Ir
Where:
V = terminal potential difference across the battery
ε = e.m.f. of the battery
I = current flowing through the circuit
r = internal resistance
In this case, we are given:
V = 11.2V
r = 0.40Ω
R = 5.60Ω
We can calculate the current (I) by using Ohm's Law:
I = V / R
Substituting the given values:
I = 11.2V / 5.60Ω
I = 2A
Now we can substitute the values of V, I, and r into the formula V = ε - Ir, and solve for ε:
11.2V = ε - 2A * 0.40Ω
11.2V = ε - 0.8V
To solve for ε, we isolate it on one side of the equation:
ε = 11.2V + 0.8V
ε = 12V
Therefore, the e.m.f. of the battery is 12V.
To find the electromotive force (e.m.f.) of the battery, we can use Ohm's law and the concept of voltage division.
First, let's understand how the internal resistance affects the terminal potential difference across the battery. When the resistance R is connected across the terminals, the total circuit resistance becomes Rt = R + r, where r is the internal resistance of the battery.
Using Ohm's law, we can express the current flowing through the circuit as I = V / Rt, where V is the terminal potential difference across the battery.
Given that the terminal potential difference V is 11.2V, the resistance R is 5.60Ω, and the internal resistance r is 0.40Ω, we can now calculate the current I using Ohm's law:
I = V / Rt
I = 11.2V / (5.60Ω + 0.40Ω)
I = 11.2V / 6.00Ω
I ≈ 1.87A
Now, we can apply voltage division to find the potential difference across the internal resistance of the battery. The potential difference across the internal resistance, Vr, can be calculated as:
Vr = I * r
Vr = 1.87A * 0.40Ω
Vr = 0.748V
Finally, we can determine the e.m.f. of the battery by adding the potential difference across the internal resistance to the terminal potential difference:
ε = V + Vr
ε = 11.2V + 0.748V
ε ≈ 11.95V
Therefore, the e.m.f. of the battery is approximately 11.95V.