Question

Judge the equivalent resistance when the following resistances are connected in parallel: 1 ohm and 10⁶ ohm.

(a) 1Ω

(b) 10⁶Ω

(c) 0.9999995Ω

(d) 0.999999Ω

Answer 1

The equivalent resistance of a parallel circuit consisting of 1 ohm and 10⁶ ohm resistors is slightly less than 1 ohm, making option (c) 0.9999995 ohm the correct selection.

Step-by-step explanation:

When two resistances are connected in parallel, the equivalent resistance can be calculated using the formula ¹⁄₁ₓ = ¹⁄ₓₑ + ¹⁄ₓₒ. For resistances 1 ohm and 10⁶ ohm in parallel, this calculation becomes:

¹⁄ₓ = ¹⁄₁ + ¹⁄₁⁰⁶

Since 1 is much smaller than 10⁶, the equivalent resistance is just slightly less than 1 ohm but not as low as 0.999999 ohm, making (c) 0.9999995 ohm the correct answer.

The equivalent resistance in a parallel circuit is always less than the smallest resistance in the circuit because the total pathway for current is increased. Therefore, the parallel connections result in a smaller equivalent resistance compared to any individual resistor in the setup.