A hot plate of an electric oven connected to a 220V line has two resistance coils A and B, each of 24 ohms resistance, which may be used separately, in series, or in parallel. What are the currents in the cases?
In series the R is 24 ohms (R1 + R2).
In parallel the R is 12 ohms(1/R1 + 1/R2 = 1/R).
E = IR or I = E/R. You know E and R, solve for I.
To find the currents in different cases, we need to use Ohm's Law (V = I * R), where V is the voltage, I is the current, and R is the resistance.
Case 1: Coil A used separately
The resistance of coil A is 24 ohms, and the voltage is 220V.
Using Ohm's Law, we can find the current:
I = V / R
I = 220V / 24Ω
I ≈ 9.17 A
Case 2: Coil B used separately
The resistance of coil B is also 24 ohms, and the voltage is 220V.
Using Ohm's Law:
I = V / R
I = 220V / 24Ω
I ≈ 9.17 A
Case 3: Coils A and B in series
To find the equivalent resistance when two resistors are in series, we sum the individual resistances:
R_eq = R1 + R2 = 24Ω + 24Ω = 48Ω
Using Ohm's Law:
I = V / R
I = 220V / 48Ω
I ≈ 4.58 A
Case 4: Coils A and B in parallel
To find the equivalent resistance when two resistors are in parallel, we use the formula:
1/R_eq = 1/R1 + 1/R2
1/R_eq = 1/24Ω + 1/24Ω
1/R_eq = 2/24Ω
1/R_eq = 1/12Ω
R_eq = 12Ω
Using Ohm's Law:
I = V / R
I = 220V / 12Ω
I ≈ 18.33 A
So, the currents in each case are as follows:
- When using coil A separately: approximately 9.17 A
- When using coil B separately: approximately 9.17 A
- When coils A and B are in series: approximately 4.58 A
- When coils A and B are in parallel: approximately 18.33 A
To find the currents in each case, we can use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the voltage (V) across the conductor divided by its resistance (R). Mathematically, I = V/R.
First, let's calculate the current in coil A when it is used alone.
Given: Voltage (V) = 220V, Resistance (R) = 24 ohms
Using Ohm's Law, I = V/R
So, I (current in coil A when used alone) = 220V / 24 ohms ≈ 9.167A.
Next, let's calculate the current in coil B when it is used alone (same calculation as above):
I (current in coil B when used alone) = 220V / 24 ohms ≈ 9.167A.
Now, let's calculate the current when coil A and coil B are connected in series. In a series circuit, the total resistance is the sum of the individual resistances.
Given: Resistance of coil A (R1) = 24 ohms, Resistance of coil B (R2) = 24 ohms
Total resistance (RT) in series = R1 + R2 = 24 ohms + 24 ohms = 48 ohms
Using Ohm's Law, I = V/RT
So, I (current in series connection) = 220V / 48 ohms ≈ 4.583A.
Finally, let's calculate the current when coil A and coil B are connected in parallel. In a parallel circuit, the total resistance is calculated differently.
Given: Resistance of coil A (R1) = 24 ohms, Resistance of coil B (R2) = 24 ohms
Total resistance (RT) in parallel = 1 / (1/R1 + 1/R2) = 1 / (1/24 + 1/24) = 1 / (2/24) = 1 / (1/12) = 12 ohms
Using Ohm's Law, I = V / RT
So, I (current in parallel connection) = 220V / 12 ohms ≈ 18.333A.
To summarize:
- Current in coil A when used alone = 9.167A
- Current in coil B when used alone = 9.167A
- Current in series connection = 4.583A
- Current in parallel connection = 18.333A