$\frac{18}{11}$ohms
Parallel Resistance Calculation for Three Wires
To find the total resistance ($R_{total}$) of resistors connected in parallel, we use the formula:
$ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $Given the resistances:
- $R_1 = 3 \Omega$
- $R_2 = 6 \Omega$
- $R_3 = 9 \Omega$
Substitute these values into the formula:
$ \frac{1}{R_{total}} = \frac{1}{3} + \frac{1}{6} + \frac{1}{9} $To add these fractions, find a common denominator, which is 18:
$ \frac{1}{R_{total}} = \frac{1 \times 6}{3 \times 6} + \frac{1 \times 3}{6 \times 3} + \frac{1 \times 2}{9 \times 2} $ $ \frac{1}{R_{total}} = \frac{6}{18} + \frac{3}{18} + \frac{2}{18} $Add the numerators:
$ \frac{1}{R_{total}} = \frac{6 + 3 + 2}{18} $ $ \frac{1}{R_{total}} = \frac{11}{18} $Finally, invert the result to find the total resistance ($R_{total}$):
$ R_{total} = \frac{18}{11} \Omega $Therefore, the total resistance of the circuit is $\frac{18}{11}$ ohms.
Similar Questions
- Which of the following devices is used to convert alternating current into direct current?
- Which one is not a good conductor of electricity?
According to Joule's law of heating, heat produced in a resistor is expressed by which relation?
Electrical conductors are materials that possess which of the following properties?
When considering the dimensions of electric charge, which fundamental units must be combined to express it in terms of SI base quantities?
What change occurs in the amount of heat produced when the electric current in a conductor is doubled?
If you measure the amount of electric charge flowing in a circuit, which SI unit would you use to record the result?
The quantity represented by the unit volt per ampere corresponds to which electrical unit?
Important Questions from Current Electricity
The property of electric current which is applicable in the fuse wires is
An electric current is expressed by a unit called .
What do you call a component of identical size that offers a higher resistance to electricity?
Identify the correct statement.
_______ is a simple device that is used to either break the electric circuit, or to complete it.
