In the given circuit, the resistance R has a value that depends on the current. Specifically, R is 20 ohms when I is zero, and the increase in resistance (in ohms) is numerically equal to one-half of the current in amperes. What is the value of current I in the circuit?
Correct answer: B. 10 amp
- A. 8.33 amp
- B. 10 amp
- C. 12.5 amp
- D. 18.5 amp
Explanation
To find the current I, start by expressing the resistance R as a function of current: R = 20 + 0.5I, where 20 ohms is the base resistance and 0.5I accounts for the increase per ampere of current. According to Ohm's Law, V = IR, where V is voltage. Rearrange this equation to find I in terms of R. Substitute the expression for R into your equation and solve for I. You will find that I = 10 amps satisfies the equation, hence Option B is correct. Other options do not satisfy the relationship described in the problem statement.
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