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Elizabeth is good. She's moral. She's upright. She's composed. And she's also colder than Salem, Massachusetts, in early February.
In a neat literary twist, Elizabeth's positive qualities are also her negative ones. She is a virtuous woman who is steadfast and true—but these traits also make her a bit of a cold fish. When we first meet her, she's especially cold...and thinks she smells something fishy. She's got good reason to be suspicious and kind of distant, though: her husband has recently had an affair with their housekeeper, Abigail Williams:
ELIZABETH: You were alone with her?
PROCTOR, stubbornly: For a moment alone, aye.
ELIZABETH: Why, then, it is not as you told me.
PROCTOR, his anger rising: For a moment, I say. The others come in soon after.
ELIZABETH, quietly—she has suddenly lost all faith in him: Do as you wish, then. [...]
PROCTOR: Woman. (She turns to him.) I'll not have your suspicion any more.
ELIZABETH, a little loftily: I have no—
PROCTOR: I'll not have it!
ELIZABETH: Then let you not earn it. (II.65-74)
Elizabeth's reaction to the affair also reveals a bit of a vindictive streak. When she discovered her husband's sin, she gave Abby the boot and then proceeded to drop a few hints around town that the girl was a floozy. (Um, isn't John a little responsible, too?)
For the most part, though, Elizabeth is a stand-up woman. Throughout the play, she seems to be struggling to forgive her husband and let go of her anger. And, of course, her hatred of Abigail is understandable. Elizabeth's dislike of Abigail gets justified later on in the play when Abigail tries to murder Elizabeth by framing her for witchcraft.
Overall, Elizabeth is a blameless victim. The only sin we see her commit is when she lies in court, saying that John and Abigail's affair never happened. This is supposedly the only time she's ever lied in her life. Unfortunately, this is really bad timing. Though she lies in an attempt to protect her husband, it actually ends up damning him.
After she’s spent a few months alone in prison, Elizabeth comes to her own realization: she was a cold wife, and it was because she didn’t love herself that she was unable to receive her husband’s love. She comes to believe that it is her coldness that led to John's affair with Abigail:
ELIZABETH, upon a heaving sob that always threatens: John, it come to naught that I should forgive you, if you'll not forgive yourself. (Now he turns away a little, in great agony.) It is not my soul, John, it is yours. [...] Only be sure of this, for I know it now: Whatever you will do, it is a good man does it. (He turns his doubting, searching gaze upon her.) I have read my heart this three month, John. [...] I have sins of my own to count. It needs a cold wife to prompt lechery. [...] John, I counted myself so plain, so poorly made, no honest love could come to me! Suspicion kissed you when I did; I never knew how I should say my love. It were a cold house I kept! (IV.205-210)
This realization helps Elizabeth forgive her husband, and relinquishing her anger seems to bring her a measure of personal peace. Elizabeth's noblest act comes in the end when she helps the tortured John Proctor forgive himself just before his death.