Federal Reserve Chairwoman Janet Yellen is returning to Capitol Hill this week at a low point in her tenure for the relationship between her agency and Congress, with hearings scheduled in the House and Senate.

The Fed chief is required by law to testify on monetary policy before both chambers. Otherwise, Yellen might be inclined to sit out what are sure to be tough questions from Republicans hostile to the Fed.

She will testify before the House Financial Services Committee on Wednesday morning, and then the Senate Banking Committee Thursday. The Financial Services Committee will get warmed up on Tuesday with a hearing called "Fed Oversight: Lack of Transparency and Accountability" featuring some of the most prominent critics of the Fed.

While Republicans grill Yellen, investors will be watching closely for any hints she might give about the Fed's monetary policy plans. Financial companies, meanwhile, will be hoping for clarity about her plans for implementing the big regulations the agency is working on. Here are the biggest questions heading into the week:

1. How will Yellen respond to GOP charges of obstruction in the leak investigation?

Yellen and Republicans on the Financial Services panel exchanged a series of successively more hostile letters last month over the Fed's response to a 2012 leak of monetary policy deliberations.

Chairman Jeb Hensarling, R-Texas, and oversight subcommittee Chairman Sean Duffy, R-Wis., accused Yellen of "willful obstruction" in keeping documents related to their investigation from them. Yellen responded with the bureaucratic equivalent of a brush-off, saying that she couldn't provide the documents at the risk of jeopardizing a Department of Justice investigation.

Hensarling told the Wall Street Journal for an article published Monday that "we want the chair to tell the truth" and that Yellen was violating the law for not turning documents over to the committee.

The 2012 leak involved an investment newsletter publishing details about the Fed's discussions on a new round of large-scale bond purchases before an account of those discussions was supposed to be released to the public. The Fed, then run by Ben Bernanke with Yellen as vice chairwoman, reportedly breached its own protocol in not referring the investigation of the leak to its inspector general, instead trying to handle it internally.

Besides the correspondence with members of the House panel, Yellen has not had to answer questions about the leak investigation in public. That will change this week.

2. Will the Fed raise rates?

Yellen reiterated last week that she expects the economy to pick up enough for the Fed to raise rates later this year. It would be the first time since 2008 that the central bank has raised its short-term interest rate target from zero.

But although Yellen has said throughout the year that she expects rate hikes in 2015, markets don't seem to believe her.

Bond market prices indicate that investors are speculating that the Fed won't raise rates until well into 2016. That's effectively a bet that Yellen and other Fed officials are overly optimistic about the strength of the economy.

Yellen will have to defend her comments when lawmakers on both the Left and Right try to get her to commit to their preferred policy, whether that's more stimulus or raising rates quickly.

3. What's next on the Fed's regulatory agenda?

Yellen comes to the Hill as lawmakers are marking the five-year anniversary of the passage of the Dodd-Frank financial reform law, which is still bitterly opposed by many Republicans.

"We are learning that our financial system may very well be less stable under Dodd-Frank," Hensarling said Thursday, in the first in a series of hearings on the impact of the law. Hensarling is also set to give a speech on Dodd-Frank this week at the conservative nonprofit American Enterprise Institute.

Lawmakers on both sides of the aisle are likely to try to sway Yellen to their point of view in implementing the law. The Fed is working on extra capital requirements for big banks, rules on banks owning commodities and more.

Yellen is also a key member of the super-group of regulators, the Financial Stability Oversight Council, that is responsible for identifying threats to the financial system that arise outside banks and subjecting them to added oversight. The group is considering whether and how to step up regulation on asset management, a decision that many representatives and senators are eager to influence.