Question
Download Solution PDFTwo resistors, each of 10 Ω, are connected in parallel. This combination is then connected in series with a third 10 Ω resistor and a 6 V battery. The current in the circuit is ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Ohm's law: It states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature, remain constant.
- Mathematically, current-voltage can be written as V = IR, where V = Voltage, I = Current, R = Resistance
- For equivalent resistance in parallel combinations
- \(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\)
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For equivalent resistance in series combinations
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Req = R1 + R2 + . . . . + Rn
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Calculation:
Two resistors, each of 10 Ω, are connected in parallel. This combination is then connected in series with a third 10 Ω resistor and a 6 V battery. The current in the circuit is ______.
Given, Resistance, R1 = 10 Ω, R2 = 10 Ω, Battery, V = 6 volt
The resistor is connected in parallel combination,
In parallel combination, \(\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}\)
\(\frac{1}{R_p}=\frac{1}{10}+\frac{1}{10}\)
RP = 5 Ω
Now, the resistance RP is connected in series with 10 Ω,
Req = 5 + 10 = 15 Ω
Current in the circuit, \(I=\frac{V}{R}=\frac{6}{15}=0.4~A\)
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