In a circuit with a 24V, 20-ohm contactor coil wired in series with a 24V, 200-ohm control relay across a 24V supply, which device energizes?

• A. The 24V, 20-ohm contactor coil energizes
• B. The 24V, 200-ohm control relay energizes
• C. Both energize
• D. Neither energizes

Answer: (B)

When two devices are wired in series across the same 24 V supply, the current through both is the same and the voltage from the supply is divided between them in proportion to their resistances. The higher-resistance device will drop more of the supply voltage, leaving the lower-resistance device with a smaller share.

Compute the current in the loop: total resistance is 20 + 200 = 220 ohms, so I = 24 V / 220 Ω ≈ 0.109 A (about 109 mA). The voltage across the 200-ohm control relay is V = I × 200 Ω ≈ 21.8 V. The voltage across the 20-ohm contactor coil is V = I × 20 Ω ≈ 2.2 V.

A 24 V coil typically energizes around the full supply, and 21.8 V is sufficient to pull in the 24 V control relay, whereas only about 2.2 V is across the contactor coil—far below what it needs to energize. Thus the control relay energizes while the contactor coil does not.