© All Rights reserved @ LearnWithDash
Step-by-Step Solution
Step 1: Understand the Circuit Configuration
We have two batteries, each with its own electromotive force (emf) and internal resistance, connected in parallel across a load resistor of 10 Ω. Specifically:
Battery 1 emf = 12 V, internal resistance = 1 Ω.
Battery 2 emf = 13 V, internal resistance = 2 Ω.
Load resistor RL = 10 Ω.
The key point is that both batteries, when connected in parallel, will share the same voltage across the load resistor.
Step 2: Assign Symbols and Notations
Let the voltage across the load resistor (and hence the voltage across each battery’s terminals) be $V$. Also, let the current supplied by Battery 1 be $I_1$ and the current supplied by Battery 2 be $I_2$. The total current through the load (of resistance 10 Ω) is then $I = \frac{V}{10}$.
Step 3: Write the Equations for Each Battery
For Battery 1 (emf 12 V, internal resistance 1 Ω):
$V + I_1 \times 1 = 12 \quad \Longrightarrow \quad I_1 = 12 - V$
For Battery 2 (emf 13 V, internal resistance 2 Ω):
$V + I_2 \times 2 = 13 \quad \Longrightarrow \quad I_2 = \frac{13 - V}{2}$
Step 4: Write the Load Current Relation
The total current through the load resistor is the sum of the currents from both batteries:
$I_1 + I_2 = \frac{V}{10}$
Substituting $I_1$ and $I_2$ from above, we get:
$(12 - V) + \frac{13 - V}{2} = \frac{V}{10}$
Step 5: Solve for the Load Voltage $V$
First, multiply everything by 2 to clear the fraction in the second term on the left side:
$2(12 - V) + (13 - V) = \frac{2V}{10}$
Which simplifies to:
$24 - 2V + 13 - V = \frac{2V}{10}$
Combine like terms on the left side:
$37 - 3V = \frac{2V}{10}$
Multiply both sides by 10 to clear the fraction:
$10 \times \bigl(37 - 3V\bigr) = 2V$
$370 - 30V = 2V$
Bring the terms involving $V$ together:
$370 = 32V$
Therefore,
$V = \frac{370}{32} = 11.5625 \approx 11.56 \text{ V}$
Step 6: Interpret the Result
The computed voltage across the load ($ \approx 11.56\text{ V}$) lies between 11.5 V and 11.6 V, matching the given correct option.
Final Answer
The voltage across the load lies between 11.5 V and 11.6 V.
Reference Image
