Resistors of 30 ohms and 60 ohms are connected in parallel and joined in series to a 10 ohm resistor.
The circuit voltage is 180 volts.
Find:
the voltage of the parallel circuit
the voltage across the parallel circuit
the current through the 10 ohm resistor
The two parallel resistors behave like a single serives resistor of equivalent resistance Req
1/Req = 1/30 + 1/60 = 1/20
So Req = 20 ohms
The total circuit current is
V/R = 180/(20 + 10) = 6 Amps
The voltage drop is 60 V across the 10 ohm resistor and 120 V across the pair of parallel resistors. You seem to be asking the same question twice.
All of the circuit current (6A) goes through the 10 ohm resistor
To find the voltage of the parallel circuit:
1. Calculate the total resistance of the parallel circuit.
Use the formula: (1 / total resistance) = (1 / resistor 1) + (1 / resistor 2) + ...
For this case, we have:
(1 / total resistance) = (1 / 30 ohms) + (1 / 60 ohms)
Simplify and solve for the total resistance:
(1 / total resistance) = (2 / 60) + (1 / 60)
(1 / total resistance) = (3 / 60)
(1 / total resistance) = (1 / 20)
total resistance = 20 ohms
2. Calculate the voltage of the parallel circuit using Ohm's Law.
Use the formula: voltage = current * resistance
Since the circuit voltage is 180 volts, and the total resistance of the parallel circuit is 20 ohms, we can rearrange the formula to solve for current:
current = voltage / resistance
current = 180 volts / 20 ohms
current = 9 amperes
3. Calculate the voltage of the parallel circuit using Ohm's Law.
Use the same formula: voltage = current * resistance
The resistance of the parallel circuit is given by the total resistance, which is 20 ohms.
Therefore, the voltage of the parallel circuit is:
voltage = current * resistance
voltage = 9 amperes * 20 ohms
voltage = 180 volts
Now, to find the voltage across the parallel circuit and the current through the 10 ohm resistor:
4. Calculate the total resistance of the series circuit.
Since the resistors are connected in series, we simply add their values:
total resistance = 30 ohms + 60 ohms + 10 ohms
total resistance = 100 ohms
5. Calculate the current through the 10 ohm resistor using Ohm's Law.
voltage = current * resistance
180 volts = current * 100 ohms
current = 1.8 amperes
The voltage across the parallel circuit is: 180 volts.
The current through the 10 ohm resistor is: 1.8 amperes.
To find the voltage of the parallel circuit, you need to compute the equivalent resistance of the parallel combination of the 30-ohm and 60-ohm resistors. The formula for calculating the equivalent resistance in a parallel combination of resistors is:
1/Req = 1/R1 + 1/R2 + ...
Let's plug in the values:
1/Req = 1/30 + 1/60
To simplify, find the least common multiple (LCM) of 30 and 60, which is 60:
1/Req = 2/60 + 1/60
1/Req = 3/60
Next, invert both sides of the equation to find Req:
Req = 60/3
Req = 20 ohms
So, the equivalent resistance of the parallel combination is 20 ohms.
Now, to find the voltage across the parallel circuit, you can use Ohm's Law, which states that voltage (V) equals current (I) multiplied by resistance (R):
V = I * R
Since the circuit voltage is 180 volts and the equivalent resistance is 20 ohms, you can rearrange the formula to solve for the current:
I = V / R
I = 180 / 20
I = 9 amps
Now that you know the current through the parallel circuit is 9 amps, you can find the voltage across it:
V_parallel = I * Req
V_parallel = 9 * 20
V_parallel = 180 volts
Therefore, the voltage of the parallel circuit is 180 volts.
Finally, to find the current through the 10-ohm resistor, you can use Ohm's Law again:
I = V / R
I = 180 / 10
I = 18 amps
Thus, the current through the 10-ohm resistor is 18 amps.