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Q. 63

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 793

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Short Answer

What is the current through the resistor in ? Is the current from left to right or right to left?

The current is from left to right.

See the step by step solution

Step by Step Solution

Step 1 : Given Information 

We need to find the current from left to right or right to left.

Step 2: Explanation

We will apply the loop rule where the loop rule is the statement that the electrostatic force is conservative. Suppose we go around a loop, measuring potential differences across circuit elements as we go and the algebraic sum of these differences is zero when we return to the starting point.

Let us draw a loop clockwise and apply equation for the upper loop, where the voltage across the resistor is positive because the traveling direction is in the opposite direction of the current. The are negative because the direction of traveling is from positive to negative terminal in the battery

Where is the current in the upper branch and is the current in the middle branch, for the bottom loop, we apply loop rule clockwise, where the voltage across the resistor is negative because the travelling direction is in the opposite direction of the current and is positive because the travelling direction is in the opposite direction of the current. The is positive because the direction of traveling is from negative to positive terminal in the battery and are negative because the direction of traveling is from positive to negative terminal in the battery

Where is the current in the bottom branch. From junction rule, we get that the current through the bottom branch is

Step 3 : Simplification

Now, Let us plug the expression of into equation (3) to get

Let us subtract the two equations to get the middle current by

Therefore, we get the middle current by

This is the current through the resistor and its direction is from left to right.

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