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.