<form method="post" action="#">
  
  <h4>Which do you like more?</h4>
  <div>
    <div>
      <input type="radio" name="choice-animals" id="choice-animals-dogs" required>
      <label for="choice-animals-dogs">I like dogs more</label>
    
      <div class="reveal-if-active">
        <label for="which-dog">Good call. What's the name of your favorite dog?</label>
        <input type="text" id="which-dog" name="which-dog" class="require-if-active" data-require-pair="#choice-animals-dogs">
      </div>
    </div>
    
    <div>
      <input type="radio" name="choice-animals" id="choice-animals-cats">
      <label for="choice-animals-cats">I like cats more</label>
    
      <div class="reveal-if-active">
        <label for="which-cat">Why? Cats are weird. Respond.</label>
        <input type="text" id="which-cat" name="which-cat" class="require-if-active" data-require-pair="#choice-animals-cats">
      </div>
    </div>
  </div>
  
  <h4>Would you like a dollar?</h4>
  <div>
    <input type="checkbox" name="choice-dollar" id="choice-dollar">
    <label for="choice-dollar">Sure.</label>

    <div class="reveal-if-active">
      Wouldn't we all.
    </div>
  </div>
  
  <div>
    <input type="submit" value="Submit">
  </div>
      
</form>
.reveal-if-active {
  opacity: 0;
  max-height: 0;
  overflow: hidden;
  font-size: 16px;
  transform: scale(0.8);
  transition: 0.5s;
  
  label {
    display: block;
    margin: 0 0 3px 0;
  }
  input[type=text] {
    width: 100%;
  }
  
  input[type="radio"]:checked ~ &,
  input[type="checkbox"]:checked ~ & {
    opacity: 1;
    max-height: 100px;
    padding: 10px 20px;
    transform: scale(1);
    overflow: visible;
  }
  
}

form {
  max-width: 500px;
  margin: 20px auto;
  > div {
    margin: 0 0 20px 0;
    label {
      font-weight: bold;
    }
    > div {
      padding: 5px;
    }
  }
  > h4 {
    color: green;
    font-size: 24px;
    margin: 0 0 10px 0;
    border-bottom: 2px solid green;
  }
}

body {
  font-size: 20px;
}
* {
  box-sizing: border-box;
}
View Compiled
var FormStuff = {
  
  init: function() {
    this.applyConditionalRequired();
    this.bindUIActions();
  },
  
  bindUIActions: function() {
    $("input[type='radio'], input[type='checkbox']").on("change", this.applyConditionalRequired);
  },
  
  applyConditionalRequired: function() {
  	
    $(".require-if-active").each(function() {
      var el = $(this);
      if ($(el.data("require-pair")).is(":checked")) {
        el.prop("required", true);
      } else {
        el.prop("required", false);
      }
    });
    
  }
  
};

FormStuff.init();

External CSS

This Pen doesn't use any external CSS resources.

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js