Two circuits each contain resistors whose temperature coefficients are +α and -α, both initially R₀. Circuit A has them in series and circuit B has them in parallel, both on fixed-voltage supplies. What happens to currents Iₐ and Iᵦ as the temperature rises? Image
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Question

Two circuits each contain resistors whose temperature coefficients are +α and -α, both initially R₀. Circuit A has them in series and circuit B has them in parallel, both on fixed-voltage supplies. What happens to currents Iₐ and Iᵦ as the temperature rises? Image

Options

G1 Physics · Accepted Answer

Step 1: For temperature increase ΔT write x = αΔT. Resistances are R₊ = R₀(1 + x), R₋ = R₀(1 − x). Step 2: In series, R_A = R₊ + R₋ = 2R₀, independent of temperature. Thus Iₐ = V/(2R₀) stays constant. Step 3: In parallel, 1/R_B = 1/[R₀(1 − x)] + 1/[R₀(1 + x)] = 2/[R₀(1 − x²)]. Step 4: Hence R_B = R₀(1 − x²)/2, which decreases as |x| grows (within the linear-resistance model). Step 5: Since Iᵦ = V/R_B, Iᵦ increases. Final answer: Iₐ constant, Iᵦ increases (Option A).

Two circuits each contain resistors whose temperature coefficients are +α and −α, both initially R₀. Circuit A has them in series and circuit B has them in parallel, both on fixed-voltage supplies. What happens to currents Iₐ and Iᵦ as the temperature rises? Image