A battery of e.m.f 24v and internal resistance of 4ohms is connected to a resistor of 3ohms.what is the terminal potential difference of the battery
I = V / (Ri + Ro) = V / 7 = 3.43Amps.
Vt = I*Ro = 3.43 * 3 = 10.3volts.
Well, if you're looking for the terminal potential difference, then it's like trying to find out how grouchy a clown is without knowing how big his nose is! You see, the terminal potential difference is the difference in potential between the battery's terminals when a current is flowing through it. In this case, we have a battery with an electromotive force (emf) of 24 volts and an internal resistance of 4 ohms, connected to a resistor of 3 ohms.
To find the terminal potential difference, we need to take into account the internal resistance. It's like trying to run through a pile of banana peels instead of straight on solid ground, it's going to slow you down!
Using Ohm's law, we know that the voltage across a resistor (V) is equal to the current (I) multiplied by the resistance (R). Since we're interested in the terminal potential difference, let's call that Vt. We can express Vt as:
Vt = emf - (I * internal resistance)
Now, we need to find the current flowing through the circuit. Using Ohm's law again, we can calculate that as:
I = emf / (resistor + internal resistance)
Plugging in the values, we get:
I = 24V / (3Ω + 4Ω)
I = 24V / 7Ω
I ≈ 3.43A
Now we can substitute the value of I back into the equation for Vt:
Vt = 24V - (3.43A * 4Ω)
Vt ≈ 24V - 13.72V
Vt ≈ 10.28V
So, the terminal potential difference of the battery is approximately 10.28 volts. Just remember, even clowns need a little bit of resistance in their lives!
To find the terminal potential difference of the battery, you can use the formula:
Vt = E - I * R
Where:
Vt is the terminal potential difference (V)
E is the electromotive force or e.m.f of the battery (V)
I is the current flowing through the circuit (A)
R is the total resistance of the circuit (ohms)
In this case, the e.m.f of the battery is given as 24V and the internal resistance is 4 ohms. The resistor connected to the battery has a resistance of 3 ohms.
To calculate the terminal potential difference, we need to find the total resistance of the circuit.
Rt = R1 + R2
Where:
Rt is the total resistance (ohms)
R1 is the resistance of the battery (internal resistance) (ohms)
R2 is the resistance connected to the battery (ohms)
In this case:
R1 = 4 ohms (internal resistance of the battery)
R2 = 3 ohms (resistor connected to the battery)
Rt = R1 + R2
Rt = 4 ohms + 3 ohms
Rt = 7 ohms
Now, we can calculate the terminal potential difference using the formula mentioned earlier:
Vt = E - I * R
Given:
E = 24V (emf of the battery)
R = Rt = 7 ohms (total resistance of the circuit)
We still need to find the current flowing through the circuit, which can be calculated using Ohm's Law:
I = V / R
Where:
I is the current flowing through the circuit (A)
V is the voltage across the circuit (V)
R is the total resistance of the circuit (ohms)
In this case:
V = E = 24V (since there are no other components in the circuit)
R = 7 ohms (total resistance of the circuit)
I = V / R
I = 24V / 7 ohms
I ≈ 3.43 A (rounded to two decimal places)
Now, we can calculate the terminal potential difference:
Vt = E - I * R
Vt = 24V - 3.43A * 7 ohms
Vt = 24V - 24.01V
Vt ≈ -0.01V
The terminal potential difference of the battery is approximately -0.01V (rounded to two decimal places).
To find the terminal potential difference of the battery, you need to understand the concept of voltage and how it interacts with resistors in a circuit.
The terminal potential difference (Vt) of a battery is the potential difference across its terminals when it is connected to a circuit. It can be calculated using Ohm's Law and the concept of voltage division.
Ohm's Law states that the current (I) flowing through a circuit is equal to the voltage (V) across the circuit divided by the total resistance (R):
I = V / R
In this given circuit, the total resistance (Rt) is the sum of the internal resistance (Ri) of the battery and the resistor connected in the circuit:
Rt = Ri + R
Substituting the given values into the equation, we have:
Rt = 4Ω + 3Ω
Rt = 7Ω
Now, we can find the current flowing through the circuit using Ohm's Law:
I = V / Rt
Substituting the values of the EMF (E) of the battery and the total resistance (Rt):
V / 7Ω = 24V / 7Ω
Cross-multiplying, we find:
V = (24V / 7Ω) * 7Ω
V = 24V
Therefore, the terminal potential difference of the battery in this circuit is 24V.