Three resistors of 4, 6 and 10 ohms are connected in parallel. If the combinatio

Question

Three resistors of 4, 6 and 10 ohms are connected in parallel. If the combination is connected in series witha  12v battery adn a 2 ohm resistor. What is the current through the 10 ohm resistor?

Explanation / Answer

If resistors are connected in parallel, they have the same voltage and the total current is divided such that each resistor has a portion of the total current. If the resistors are in series, they have the same current and the total voltage is divided such that each resistor has a portion of the total voltage. Therefore for the 3 resistors that are in parallel, we can have an equivalent resistor that will be in series with the 2Ohm resistor For resistors in parallel, --> 1/Req= 1/R1 + 1/R2 + 1/R3 +... --> 1/Req= 1/4 + 1/6 + 1/10 --> 1/Req= (15+10+6)/60 --> Req= 60/(15+10+6)= 60/31= 1.935Ohms Now to find the current that is going through both the 2Ohm resistor and Req, (since it's the same current as they're in series) For resistors in series, --> Rtotal= Req + R(of 2Ohms) --> Rtotal= 1.935 + 2 --> Rtotal= 3.935Ohms To find the current, we use the "V(voltage)= I(current) * R(resistance)" equation --> V=I*Rtotal --> I= V/Rtotal --> I= 12/3.935 --> I= 3.049Amperes And then use the "V=I*R" equation again to find the voltage across Req --> V(across Req)= I*Req --> V(across Req)= 3.049*1.935 --> V(across Req)= 5.900V OR (ANOTHER WAY TO V(ACROSS Req)) Now to find the voltage across a resistor when it's in series is, --> V1= Vtotal [R1/Rtotal] --> V(across Req)= V*[Req/Rtotal] --> V(across Req)= 12*[1.935/3.935] --> V(across Req)= 5.900V Now we look at only the parallel part of the circuit, As we said before if the resistors are in parallel then they have the same voltage --> V(across the 10Ohm resistor)= V(across Req)= 5.900V and since we know R=10Ohms Then again we just have to use "V=I*R" equation to get I --> V= I*R --> I= V/R --> I= 5.900/10 --> I= 0.590Amperes So the current that passes through the 10Ohm resistor is -->I= 0.590Amperes

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.