9780199339136, Chapter 1, Problem 10P

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Chapter 1, Problem 10P Step-by-step solution Step of 4 Refer to Figure P1.10 in the The voltage across the parallel branches remains same. Here, the voltage across the terminals of parallel branches is V. Write the expression for current, I₁ using ohms law. V (1) Write the expression for current, I₂ using ohms law. I₂ V (2) Apply Kirchhoff's current law to the circuit. = V V = I V = (3) Step 2 of 4 Substitute equation (3) in equation (1). V I = = Therefore, the current through resistor I Step 3 of 4 Substitute equation (3) in equation (2). V I = + = = Therefore, the current through resistor R2, I₂ is I Hence, current division rule was proved. Step of 4 Calculate the voltage across resistor, I₂R₂ Substitute I R2 = Therefore, the voltage expression, V is