$\frac{18}{11}$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?
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?
What change occurs in the amount of heat produced when the electric current in a conductor is doubled?
When considering the dimensions of electric charge, which fundamental units must be combined to express it in terms of SI base quantities?
- Which one is not a good conductor of electricity?
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Which of the following is a conductor of electric charge?
If you measure the amount of electric charge flowing in a circuit, which SI unit would you use to record the result?
If the resistance of a circuit is doubled, the current flowing through the circuit (keeping the voltage the same) will _____.
A.increase by half
B.decrease by half
C.remain the same
D.become zero
Important Questions from Current Electricity
Which of the following is a bad conductor of electricity?
In general, in an alternating current circuit
The laws of electromagnetic induction have been used in the construction of a
A 220 volt and 100 watt bulb is connected to a 110 volt source. The power consumption by the bulb is
Which of the following statement is correct?
I. 1 kWh = 3.6 × 10 6J.
II. The SI unit of electric current is the ampere.
