five resistors of 30 ohms each are connected in parallel across a 120 volt line. the combined resistance of the five resistors is ___ ohms.
The total current in the circuit is ___ amperes.
The current in each branch is ___ amperes.
How do I set these up:?
1/rtotal= 1/R1+ 1/r2 + ...= 5/30
Rt=6ohms
current in each resistor: 120/30=4amps
total current=120/6=20amps
To find the combined resistance of the five resistors, you can use the formula for resistors in parallel:
1/R_total = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5
Given that each resistor has a resistance of 30 ohms, we can substitute the values:
1/R_total = 1/30 + 1/30 + 1/30 + 1/30 + 1/30
Simplifying the equation:
1/R_total = 5/30
To find R_total, we can take the reciprocal of both sides:
R_total = 30/5
R_total = 6 ohms
So, the combined resistance of the five resistors is 6 ohms.
To find the total current in the circuit, we can use Ohm's Law:
Total current (I_total) = Voltage (V) / Combined Resistance (R_total)
Given that the voltage is 120 volts, and the combined resistance is 6 ohms, we can substitute the values:
I_total = 120 V / 6 ohms
I_total = 20 amperes
So, the total current in the circuit is 20 amperes.
Since the resistors are connected in parallel, the same voltage (120 volts) is applied across each resistor. Therefore, the current in each branch will be equal.
So, the current in each branch is also 20 amperes.
To solve these questions, you need to understand the concepts of resistors connected in parallel and the relationship between voltage, resistance, and current.
1. Combined Resistance:
When resistors are connected in parallel, the total resistance can be calculated using the formula:
1/RTotal = 1/R1 + 1/R2 + 1/R3 + ...
In this case, you have five resistors of 30 ohms each connected in parallel. To find the total resistance (RTotal), you can substitute the values into the formula:
1/RTotal = 1/30 + 1/30 + 1/30 + 1/30 + 1/30.
Simplifying this equation will give you the reciprocal of the total resistance (1/RTotal). Finally, take the reciprocal of 1/RTotal to find the combined resistance.
2. Total Current:
According to Ohm's Law, the relationship between voltage (V), resistance (R), and current (I) is given by the formula V = IR. Rearranging the formula, we can solve for current, I: I = V/R.
In this case, the voltage is given as 120 volts, and the combined resistance is the one you calculated in step 1. Plug these values into the formula to find the total current (I).
3. Current in Each Branch:
When resistors are connected in parallel, the current gets divided among the branches. In this case, since all the resistors are of the same value (30 ohms), the current will divide equally among them.
To find the current in each branch, you can divide the total current (which you calculated in step 2) by the number of branches (in this case, there are five resistors).
By using these steps, you can solve the given questions.