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?

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.

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.