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. Both devices energize
• C. Neither energizes
• D. The 24V, 200-ohm control relay energizes

Answer: (D)

When two 24V coils are wired in series across a 24V supply, the same current flows through both coils. The coil with the smaller resistance will drop only a small portion of the voltage, while the coil with the larger resistance will drop most of it. The total circuit resistance is 20 Ω + 200 Ω = 220 Ω, so the current is I = 24 V / 220 Ω ≈ 0.109 A. The voltage across the 20 Ω contactor coil is V = I × 20 Ω ≈ 2.18 V, which is far too low for it to energize. The voltage across the 200 Ω control relay coil is V = I × 200 Ω ≈ 21.8 V, which is close to 24 V and typically enough for a 24V coil to pull in. Therefore, the control relay energizes while the contactor coil does not.

When two 24V coils are wired in series across a 24V supply, the same current flows through both coils. The coil with the smaller resistance will drop only a small portion of the voltage, while the coil with the larger resistance will drop most of it. The total circuit resistance is 20 Ω + 200 Ω = 220 Ω, so the current is I = 24 V / 220 Ω ≈ 0.109 A. The voltage across the 20 Ω contactor coil is V = I × 20 Ω ≈ 2.18 V, which is far too low for it to energize. The voltage across the 200 Ω control relay coil is V = I × 200 Ω ≈ 21.8 V, which is close to 24 V and typically enough for a 24V coil to pull in. Therefore, the control relay energizes while the contactor coil does not.