You have 20 and 80 (unit is the upside down U) resistors in a circuit with a 100 V battery.
A)These resistors are parallel. Find the current through each resistor and the voltage drop across each resistor.
B) These resistors are connected in series. Find the current through each resistor and the voltage drop across each resistor.
The upside down U is an omega and means ohms.
A) The current though each resistor is V/R. Each has the same value of V (100 V) across it.
B) The resistance of the two resistors add up to an effective circuit resistance of Rtotal = 100 ohms.
I = V/Rtotal
use that value of I for the individual voltage drops. The same current goes through both when they are in series.
A) To find the current through each resistor and the voltage drop across each resistor in a parallel circuit, you can use the following formulas:
1. Calculate the total resistance (Rp) of the parallel circuit:
1/Rp = 1/R1 + 1/R2 + ... + 1/Rn
For two resistors in parallel, it becomes:
1/Rp = 1/R1 + 1/R2
In this case:
1/Rp = 1/20 + 1/80
Calculate Rp:
1/Rp = (80 + 20)/(20*80) = 100/1600 = 1/16
Therefore, Rp = 16
2. Calculate the total current (It) flowing through the circuit:
It = V/Rp
Where V is the voltage of the battery.
In this case:
V = 100 V
It = 100/16 = 6.25 A
3. Calculate the individual current (I1, I2) flowing through each resistor:
Since the resistors are in parallel, they have the same voltage across them.
I1 = I2 = It = 6.25 A
4. Calculate the voltage drop across each resistor (V1, V2):
V1 = R1 * I1 = 20 * 6.25 = 125 V
V2 = R2 * I2 = 80 * 6.25 = 500 V
Therefore, the current through each resistor is 6.25 A, and the voltage drop across the 20 Ω resistor is 125 V and the voltage drop across the 80 Ω resistor is 500 V.
B) To find the current through each resistor and the voltage drop across each resistor in a series circuit, you can use the following formulas:
1. Calculate the total resistance (Rs) of the series circuit:
Rs = R1 + R2 + ... + Rn
For two resistors in series, it becomes:
Rs = R1 + R2
In this case:
Rs = 20 + 80 = 100
2. Calculate the total current (It) flowing through the circuit:
Using Ohm's Law: V = I * Rs, where V is the battery voltage.
In this case:
V = 100 V
Rs = 100 Ω
Therefore, It = V / Rs = 100 / 100 = 1 A
3. Calculate the individual current (I1, I2) flowing through each resistor:
Since the resistors are in series, they have the same current flowing through them.
I1 = I2 = It = 1 A
4. Calculate the voltage drop across each resistor (V1, V2):
V1 = R1 * I1 = 20 * 1 = 20 V
V2 = R2 * I2 = 80 * 1 = 80 V
Therefore, the current through each resistor is 1 A, and the voltage drop across the 20 Ω resistor is 20 V, and the voltage drop across the 80 Ω resistor is 80 V.