Q79
General SciencePhysics
Combine three resistors 5 Ω, 4.5 Ω and 3 Ω in such a way that the total resistance of this combination is maximum with value
- a.12.5 Ω
- b.13.5 Ω
- c.14.5 Ω
- d.16.5 Ω
Answer: (A) 12.5 Ω
Resistance is greatest when all resistors are joined in series, where the values simply add: $R_s=5+4.5+3=12.5\ \Omega$. In parallel the equivalent resistance is always less than the smallest resistor: $\dfrac{1}{R_p}=\dfrac{1}{5}+\dfrac{1}{4.5}+\dfrac{1}{3}$ gives about $1.3\ \Omega$. No mixed arrangement can exceed the series value, so 13.5, 14.5 and 16.5 Ω are impossible. Remember: in series the current is the same through each resistor; in parallel the voltage is the same across each, which is why household appliances are wired in parallel.