In the given circuit the diode \( D_1 \) and \( D_2 \) have the forward resistance 250 \(\Omega\) and infinite backward resistance. When they are connected to the source as shown, the current passing through the 175 \(\Omega\) resistor is:
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In circuits with diodes and resistors, use Ohm's law to calculate total current, and the voltage divider rule to determine the current through individual resistors in series.
In this circuit, we have two diodes \( D_1 \) and \( D_2 \), with forward resistance of 250 \(\Omega\) and infinite backward resistance.
The total resistance in the circuit can be calculated by first considering the diodes' behavior. Since the diodes have infinite backward resistance, they essentially act like open circuits in the reverse direction.
Now, considering the forward resistances of the diodes and the resistors:
- The total resistance \( R_{\text{total}} \) in the circuit will be the sum of the resistances of the 50 \(\Omega\) resistor, the 55 \(\Omega\) diode resistance, and the 175 \(\Omega\) resistor in series.
Thus, the total resistance \( R_{\text{total}} \) is:
\[
R_{\text{total}} = 50 + 55 + 175 = 280 \, \Omega
\]
Now, we can calculate the total current using Ohm's law:
\[
I = \frac{V}{R_{\text{total}}}
\]
where:
- \( V = 10 \, \text{V} \) is the voltage of the source,
- \( R_{\text{total}} = 280 \, \Omega \) is the total resistance.
Substituting the values:
\[
I = \frac{10}{280} \approx 0.0357 \, \text{A}
\]
However, this is the total current. The current passing through the 175 \(\Omega\) resistor can be found using the voltage divider rule. The current passing through the 175 \(\Omega\) resistor will be the fraction of the total current corresponding to the voltage across the 175 \(\Omega\) resistor.
The voltage across the 175 \(\Omega\) resistor is:
\[
V_{175} = I \times 175 = 0.0357 \times 175 = 6.25 \, \text{V}
\]
Finally, the current passing through the 175 \(\Omega\) resistor is:
\[
I_{175} = \frac{V_{175}}{175} = \frac{6.25}{175} = 0.004 \, \text{A}
\]
Thus, the current passing through the 175 \(\Omega\) resistor is \( 0.004 \, \text{A} \).
