Two 7.4 resistors are connected in parallel, as are two 4.9 resistors. These two combinations are then connected in series in a circuit with a 11 battery.
What is the current in each resistor?
What is the voltage across each resistor?
I will start you: the two 4.9 in parallel is 4.9/2 ohms. Now add that to the two 7.9 in parallel, and ...
Three 10-Ohm resistors are connected in series to a 30-V battery. If the current in the circuit is 1 A, the total resistance in the circuit is _____ ohms.
To determine the current in each resistor, we first need to calculate the total resistance of each parallel combination of resistors. We can use the formula for resistors in parallel, which states that the total resistance (RT) of two resistors (R1 and R2) in parallel is given by:
1/RT = 1/R1 + 1/R2
Let's calculate the total resistance for the two 7.4 Ω resistors in parallel. Using the formula:
1/RT = 1/R1 + 1/R2
1/RT = 1/7.4 + 1/7.4
1/RT = 2/7.4
RT/1 = 7.4/2
RT = 7.4/2
RT = 3.7 Ω
Similarly, let's calculate the total resistance for the two 4.9 Ω resistors in parallel:
1/RT = 1/R1 + 1/R2
1/RT = 1/4.9 + 1/4.9
1/RT = 2/4.9
RT/1 = 4.9/2
RT = 4.9/2
RT = 2.45 Ω
Next, we need to calculate the total resistance of the circuit when the two parallel combinations are connected in series. The formula for resistors in series states that the total resistance (RT) in a circuit with two resistors (R1 and R2) in series is given by:
RT = R1 + R2
In this case, the total resistance of the circuit will be the sum of the resistances of the two parallel combinations:
RT = (resistance of two 7.4 Ω resistors) + (resistance of two 4.9 Ω resistors)
RT = 3.7 Ω + 2.45 Ω
RT = 6.15 Ω
Now, we can calculate the current in each resistor using Ohm's Law, which states that the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R):
I = V/R
Given that the battery has a voltage of 11 V, we can calculate the current in each resistor:
Current in 7.4 Ω resistors:
I = 11 V / 3.7 Ω
I ≈ 2.97 A
Current in 4.9 Ω resistors:
I = 11 V / 2.45 Ω
I ≈ 4.49 A
To find the voltage across each resistor, we can multiply the current in each resistor by its respective resistance using Ohm's Law:
Voltage across 7.4 Ω resistors:
V = I * R
V = 2.97 A * 7.4 Ω
V ≈ 21.96 V
Voltage across 4.9 Ω resistors:
V = I * R
V = 4.49 A * 4.9 Ω
V ≈ 21.94 V
Therefore, the current flowing through each of the 7.4 Ω resistors is approximately 2.97 A, and the current flowing through each of the 4.9 Ω resistors is approximately 4.49 A. The voltage across each of the 7.4 Ω resistors is approximately 21.96 V, and the voltage across each of the 4.9 Ω resistors is approximately 21.94 V.