Electrical Circuits and Ohm's Law Flashcards

A battery with an EMF of 24V and internal resistance of 2Ω is connected to an external load resistor. If the power dissipated inside the battery's internal resistance exactly equals the power delivered to the external load, what is the value of the external load resistance?

Answer: 2Ω

Power in the internal resistance equals I²r and power in the load equals I²R. Setting them equal gives I²r = I²R, so r = R. Since internal resistance r = 2Ω, the external load must also be 2Ω. This is also the condition for 50% efficiency — notably different from the maximum power transfer condition, which independently requires R_load = r_internal for the same reason.

Two batteries are connected in a series loop in opposing directions: Battery A has EMF = 30V with internal resistance 1Ω, and Battery B has EMF = 18V with internal resistance 0.5Ω. A single external resistor of 8.5Ω connects them. What is the steady-state current magnitude flowing in the loop?

Answer: 1.2A

When batteries oppose each other, the net EMF is the difference: 30V − 18V = 12V. The total resistance in the loop is the sum of all resistances: 1Ω + 0.5Ω + 8.5Ω = 10Ω. Applying Ohm's Law: I = 12V ÷ 10Ω = 1.2A. The current flows in the direction dictated by the dominant battery (Battery A).

A Thevenin equivalent circuit has V_th = 20V and R_th = 5Ω. A variable load resistor R_L is connected across the output terminals. What value of R_L draws the maximum possible power, and what is that maximum power?

Answer: R_L = 5Ω, P_max = 20W

The Maximum Power Transfer Theorem states maximum power is delivered when R_L = R_th = 5Ω. At this condition, current I = 20V ÷ (5+5) = 2A, and P_max = I² × R_L = 4 × 5 = 20W. Note that R_L = 0Ω would maximize current but delivers zero power to the load (P = I²× 0). The formula shortcut is P_max = V_th² ÷ (4 × R_th) = 400 ÷ 20 = 20W.

A tungsten filament measures 20Ω at 20°C. Its temperature coefficient of resistance is α = 0.0045 /°C. When the lamp is at normal operating brightness, its resistance measures 320Ω. What is the approximate filament operating temperature?

Answer: 3353°C

Using R = R₀[1 + α(T − T₀)]: 320 = 20[1 + 0.0045(T − 20)]. Dividing both sides by 20 gives 16 = 1 + 0.0045(T − 20). Subtracting 1: 15 = 0.0045(T − 20). Dividing: T − 20 ≈ 3333°C, so T ≈ 3353°C. This is physically realistic — tungsten filaments operate near 3000°C, explaining why tungsten (melting point ~3422°C) is chosen for incandescent lamps.

In a Wheatstone bridge circuit, resistors are arranged so that R₁ = 100Ω and R₂ = 250Ω form one pair of adjacent arms, and R₃ = 180Ω occupies one of the remaining arms. For the galvanometer to read exactly zero (bridge balanced), what must R₄ equal?

Answer: 450Ω

A Wheatstone bridge is balanced when R₁/R₂ = R₃/R₄, meaning the ratio of resistances in each branch is equal. Rearranging: R₄ = R₃ × (R₂/R₁) = 180 × (250/100) = 180 × 2.5 = 450Ω. A common error is inverting the ratio or confusing which arms are adjacent — the balance condition requires the cross-product equality R₁ × R₄ = R₂ × R₃.

Three identical 12Ω resistors can be wired in four distinct configurations. Ranked from highest to lowest total resistance, which configuration produces the SECOND-highest equivalent resistance?

Answer: Two resistors in parallel, with that parallel combination in series with the third

Computing each configuration: (A) All series: 12+12+12 = 36Ω — highest. (B) Two in parallel then series with third: (12‖12) + 12 = 6 + 12 = 18Ω — second highest. (C) One in parallel with the series pair: 12‖(12+12) = 12‖24 = (12×24)/(12+24) = 288/36 = 8Ω — third. (D) All in parallel: 12/3 = 4Ω — lowest. The second-highest is configuration B at 18Ω.