Find the voltage across each resistor in a series circuit. Note: R is the lowest value and all others are multiples of that value as indicated.
(there is no diagram for this circuit)
double battery cell = 15v
resistor1 = R
resistor2 = 2R
resistor3 = 4R
my answer is
1r+2r+4r=7r
15v(r/7r)
15v(2r/7r)
15v(4r/7r)
I = E/(R+2R+4R) = 15/7R = Current through each resistor.
V1 = I*R1 = 15/7R * R = 15/7 volts.
V2 = I*R2 = 15/7R * 2R = 30/7 volts.
V3 = I*R3 =15/7R * 4R = 60/7 volts.
Check: V1 + V2 + V3 = 15/7 + 30/7 + 60/7 = 105/7 = 15 volts.
Oh, you're in a series circuit! Let's see if we can find the voltage across each resistor. Here's the funny part: it's a bit like a math problem, but with a twist of humor!
So, let's start solving this circuit conundrum. We have a double battery cell that gives out 15 volts. Now, since the resistors are in series, the total resistance is the sum of all the resistors.
In this case, we have R for the first resistor, 2R for the second, and 4R for the third. So if we add them up, we get 7R.
Now, we can use Ohm's Law to find the voltage across each resistor. According to Ohm's Law, V = IR, where V is the voltage, I is the current, and R is the resistance.
Since the resistors share the same current in a series circuit, we only need to find the total current flowing through the circuit, and then we can use that current to calculate the voltage across each resistor.
But alas, we don't know the current, so we need to find that too. Well, in a series circuit, the current is the same at all points. So let's use the good old Ohm's Law again, but this time rearrange the equation to solve for current: I = V/R.
Now, if we divide the voltage of the battery cell (15 volts) by the total resistance (7R), we'll get the current flowing through the circuit.
Once we have the current, we can use it with each resistor's value to calculate the voltage drop across each. So, we'll multiply the current by the resistance of each individual resistor.
For the first resistor (R), it would be (15V * R) / 7R.
For the second resistor (2R), it would be (15V * 2R) / 7R.
And for the third resistor (4R), it would be (15V * 4R) / 7R.
Voila! We found the voltage across each resistor in our series circuit, all in a mathematically humorous way.
To find the voltage across each resistor in a series circuit, we need to use Ohm's Law, which states that the voltage across a resistor (V) is equal to the product of the current (I) flowing through the resistor and its resistance (R).
In a series circuit, the current is the same through all the resistors. In this case, let's assume the current flowing through the circuit is I.
Now, let's calculate the voltage across each resistor:
1. Resistor1 (R): The voltage (V1) across Resistor1 is equal to the current (I) multiplied by its resistance (R). So, V1 = I * R.
2. Resistor2 (2R): The voltage (V2) across Resistor2 is equal to the current (I) multiplied by its resistance (2R). So, V2 = I * 2R.
3. Resistor3 (4R): The voltage (V3) across Resistor3 is equal to the current (I) multiplied by its resistance (4R). So, V3 = I * 4R.
So, the voltage across each resistor can be expressed as:
V1 = I * R,
V2 = I * 2R,
V3 = I * 4R.
Note: In a series circuit, the sum of the voltage drops across each resistor should equal the total voltage across the circuit. In this case, the total voltage is 15V (the double battery cell).
Hope this clarifies the steps to find the voltage across each resistor in a series circuit!
To find the voltage across each resistor in a series circuit, you can follow these steps:
1. First, calculate the total resistance in the circuit by summing up the individual resistances. In this case, the total resistance (R_total) is equal to R + 2R + 4R, which simplifies to 7R.
2. Next, calculate the current (I) flowing through the circuit using Ohm's Law, which states that V = I * R, where V is the voltage and R is the resistance. In this case, we know the voltage from the battery is 15V. So, I = V / R_total = 15V / 7R.
3. With the current calculated, you can determine the voltage drop across each resistor. Since it is a series circuit, the total voltage (V_total) is equal to the sum of the voltage drops across each resistor.
- Voltage across resistor 1 (V1) = I * R = (15V / 7R) * R = (15V * R) / 7R = 15V / 7
- Voltage across resistor 2 (V2) = I * R = (15V / 7R) * 2R = (15V * 2R) / 7R = 30V / 7
- Voltage across resistor 3 (V3) = I * R = (15V / 7R) * 4R = (15V * 4R) / 7R = 60V / 7
So, the voltage across each resistor in this series circuit is:
- Voltage across resistor 1 (R) is 15V / 7.
- Voltage across resistor 2 (2R) is 30V / 7.
- Voltage across resistor 3 (4R) is 60V / 7.