A 32.0 resistor is connected in parallel to a 18.0 resistor. These are joined in series to a 3.0 resistor and a source with a potential difference of 30.0 V.
(c) Calculate the current in each resistor.
A (32.0 resistor)
A (18.0 resistor)
Calculate the potential difference across each resistor.
V (32.0 resistor)
V (18.0 resistor)
total R=3+18*32/(50)=3+11.52=14.52
total I=30/14.52
current in 32ohm= V/32=(30/14.52) (11.42)/32
current in 18 ohm=V/32=(30/14.52)(11.42)/18
Vparallel=(30/14.52)(11.42)
for the 32 and 18 in parallel
1/R = 1/32 + 1/18 ----> R = 11.5
total Resistance = 11.5 + 3 = 14.5
total i = 30/14.5 = 2.07 amps
so
i through 3 ohms = 2.07
so V drop over 3 ohms = 2.07*3 = 6.14 volts
so V drop over two in parallel = 30-6.14
= 23.9 volts
so current through 32 = 23.9/32 = 0.747amp
through 18 = 23.9/18 = 1.33 amp
To calculate the current in each resistor, we need to apply Ohm's Law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by its resistance (R).
For the 32.0Ω resistor:
I = V / R
I = 30.0 V / 32.0 Ω
I ≈ 0.938 A
For the 18.0Ω resistor:
I = V / R
I = 30.0 V / 18.0 Ω
I ≈ 1.667 A
Therefore, the current in the 32.0Ω resistor is approximately 0.938 A, and the current in the 18.0Ω resistor is approximately 1.667 A.
To calculate the potential difference across each resistor, we can use Ohm's Law again.
For the 32.0Ω resistor:
V = I * R
V = 0.938 A * 32.0 Ω
V ≈ 30.0 V
For the 18.0Ω resistor:
V = I * R
V = 1.667 A * 18.0 Ω
V ≈ 30.0V
Therefore, the potential difference across both the 32.0Ω resistor and the 18.0Ω resistor is approximately 30.0 V.
To calculate the current in each resistor in this circuit, we can use Ohm's Law, which states that current (I) is equal to the potential difference (V) across a resistor divided by its resistance (R).
For the 32.0 Ω resistor (A), we can use the total potential difference of 30.0 V. Therefore, the current through this resistor can be calculated as:
I(A) = V(A) / R(A)
I(A) = 30.0 V / 32.0 Ω
I(A) = 0.9375 A
So, the current in the 32.0 Ω resistor (A) is 0.9375 A.
Similarly, for the 18.0 Ω resistor, we can again use the total potential difference:
I(B) = V(A) / R(B)
I(B) = 30.0 V / 18.0 Ω
I(B) = 1.6667 A
Therefore, the current in the 18.0 Ω resistor (B) is 1.6667 A.
To calculate the potential difference across each resistor, we can use Ohm's Law again. The potential difference across a resistor is equal to the current through it multiplied by its resistance.
For the 32.0 Ω resistor (A), we already know the current is 0.9375 A:
V(A) = I(A) * R(A)
V(A) = 0.9375 A * 32.0 Ω
V(A) = 30.0 V
So, the potential difference across the 32.0 Ω resistor (A) is 30.0 V.
Similarly, for the 18.0 Ω resistor (B), we know the current is 1.6667 A:
V(B) = I(B) * R(B)
V(B) = 1.6667 A * 18.0 Ω
V(B) = 30.0 V
Hence, the potential difference across the 18.0 Ω resistor (B) is also 30.0 V.