Question

In the given circuit, the current flowing through the resistance \( 20 \Omega \) is \( 0.3 \, \text{A} \), while the ammeter reads \( 0.9 \, \text{A} \). The value of \( R_1 \) is ______ \( \Omega \).

Answer 1

Correct Answer: 30

To find the value of \( R_1 \), we analyze the circuit where two branches exist with resistances \( R_1 \) and \( 20 \Omega + 15 \Omega \) respectively. The current flowing through the \( 20 \Omega \) resistor is \( 0.3 \, \text{A} \), so the total current through that branch is \( 0.3 \, \text{A} \).
Since the ammeter reads \( 0.9 \, \text{A} \), this is the total current supplied to the whole circuit.
The current through \( R_1 \) is the difference between the total current and the current through the bypass branch:
\[ I_1 = 0.9 - 0.3 = 0.6 \, \text{A} \]
The voltage across each branch must be equal.
Using Ohm's law, voltage across the branch containing \( 20 \Omega \) and \( 15 \Omega \):
\[ V = 0.3 \times (20 + 15) = 0.3 \times 35 = 10.5 \, \text{V} \]
For \( R_1 \), using the same voltage:
\[ V = I_1 \times R_1 \Rightarrow 10.5 = 0.6 \times R_1 \]
Solve for \( R_1 \):
\[ R_1 = \frac{10.5}{0.6} = 17.5 \, \Omega \]
The calculated value of \( R_1 \), which equals \( 17.5 \, \Omega \), does not fall within the given range of 30,30 \( \Omega \). Re-evaluate the assumptions or question parameters to ensure all details were correctly considered.