Question

If \( R_c = m \times \ln \left(1 + \frac{R_m}{m} \right) \) then \( R_m \) is equal to

• A. \( R_m = \ln \left(1 + \frac{R_c}{m} \right) \)
• B. \( R_m = \ln \left(1 + \frac{R_c}{e} \right) \)
• C. \( R_m = m \left( e^{\frac{R_c}{m}} - 1 \right) \)
• D. Cannot be determined

Answer 1

The Correct Option is C

Step 1: Divide both sides by \(m\): \(\frac{R_c}{m}=\ln\left(1+\frac{R_m}{m}\right)\).
Step 2: Exponentiate: \(e^{R_c/m}=1+\frac{R_m}{m}\).
Step 3: Solve for \(R_m\): \(R_m=m\left(e^{R_c/m}-1\right)\).
\[ \boxed{R_m=m\left(e^{R_c/m}-1\right)} \]